Time in Hex is under the control of the God-Machine, via the Infrastructure embedded in the walls of the city. It's specifically within the city that time is controlled, though that includes all sub-planes such as the Underworld and the spirit world, as well as personal hiding spaces such as Hollows or boltholes. Characters with any kind of internal time sense will find that any objective measure of time (such an an android's internal clock) will also return to the previous time.
Outside of the player characters, the people of Hex generally don't notice that anything has changed. Demons, with their perfect recall, and stigmatics (including the characters) can remember the time that was erased, excepting the minor disruptions related to character deaths (see below). Some people, especially those involved with the supernatural, will get a feeling of deja vu, or otherwise feel that they know what's going to happen, but that's the extent of their experiences with strange time.
Demons know that there must be some massive Infrastructure behind this process, but aside from the gears in the walls (one of the most visible and oppressive signs of the God-Machine), they have no idea what it is. And simply trying to destroy the walls does no good - Saboteurs have tried, to their folly. The walls are well protected by guardian angels, and will immediately rewind time to heal damage to themselves if attacked. Bringing them down will take some other method.
A few particularly aware demons know that the walls sap memories, too, though few realize that their own memories are included. Demons are likely to think that their perfect recall is infallible, in comparison to the organic peoples of Hex. Still, there's enough vague awareness of the phenomenon that nightmares of forgetting are a whole distinct category for Beasts to tap into. Most mysterious is how the act of rewinding time can also influence the esoteric realms of the Hedge and the like, which don't seem to have any Infrastructure, at least so far as anyone has risked exploring.
Characters lose memories by degrees, rather than losing a single specific memory or set of memories. Many memories aren't lost at all; they are instead modified to better suit the history of Hex and those aleady within it. This memory modification is on-going for those who have been completely consumed by Hex; someone whose sibling arrives after them will have their brother or sister slotted into their memories over time. The difference between these characters and the PCs is that those fully in thrall of the God-Machine don't notice anything different or wrong about their changed memories.
Most memories are lost during the time period when time flows backwards. Something about a person's fundamental self is funneled into the motion of the gears, nearly impossible to retrieve. Hex works to prevent the deaths of thise in the city who haven't had their memories entirely drained and modified, ticking back the clock briefly to give them a second chance.
Like everything about the God-Machine, this comes at a cost. Those who die will find a little more of their memories slipped away, and even with that price paid, their survival is no certainty. The clock only moves back an hour, and only the one time - if the character can't avoid the circumstances of their death on their second, more informed chance, well, they're just a wash for the Machine, not worth the effort of trying again. At least there's always the chance that a local geist will take an interest in your sorry circumstances instead.
It is possible to regain those lost memories, but it is not a job for the faint of heart. Usually, it's accomplished by foiling Infrastructure or some other manifestation of the God-Machine. Other times, characters might find something that triggers traces of their memories in the realms surrounding the most material, normal part of Hex - brought to the surface by a nightmare in the Primordial Dream, striking like a revelation after eating some strange Hedge fruit, and so on. Most rare is the organic return of memories, as a character has a chance encounter with someone or something that reminds them strikingly of their previous life (or, perhaps, of the time they were in Hex before losing their memories in the first place). In this circumstance, it's usually an indicator that some Infrastructure in the area is damaged, and allowing the memories to leak out.
From an OOC perspective, memories are lost to the rewinding of time, character death, and certain events. They are regained by interacting with the game, either in mod events and investigations, through the course of interacting with NPC logs, and from the game as a whole completing plot objectives. Players have some freedom in choosing exactly how the returning memories manifest. In true World of Darkness tradition, character memories are presented by a ten point scale (see below). Generally, characters will not move more than one point up or down the scale at a time.
Power loss works in basically the same way as memory loss; something of the character seeps out of them and into the God-Machine, leaving them less unique, less a part of their home world and more a part of Hex. More powerful abilities tend to be lost and/or modified more quickly, though trademark abilities can persist for longer if it's a part of the character's image of themselves. Players are encouraged to use their own discretion, based on the scale below.
10 - Normal recall of the character's life and home world. Native world powers are intact. New arrivals to Hex start at this point in the scale.
9 - Some details begin to fade; usually these are not things that are immediately apparent, because they're things that aren't immediately relevant to a character's life. It's hard to notice the loss unless you're looking. Powers are still mostly intact.
8 - Memories seem to shift in setting; the events stay the same, but the environments begin to become more like those in Hex. Powers begin to weaken and shift.
7 - At this point, it's obvious to the character that something is wrong. Their powers don't quite work right, and terms unique to their world vanish like they were never there. Other characters using them sounds like nonsense. They may experience minor physical changes related to their new identity.
6 - Minor life events and people the character is only vaguely acquainted with are gone, either modified into Hex or disappeared outright. Powers that don't have a parallel ability in the World of Darkness begin to truly malfunction.
5 - At this point, the character belongs as much to Hex as they do to their home world, and their nature as a specific creature of the World of Darkness (if any) begins to become obvious. Calling for their native powers instead of the ones they're beginning to manifest becomes difficult.
4 - More major events and people start to disappear or change within the character's memory. Powers that don't fit into the World of Darkness are practically lost; the character may not even remember they exist. If the character is undergoing a physical change in the process of becoming part of Hex, they also begin to forget what they originally looked like.
3 - You know you've lost memories. You can call up major events of your old life, and sometimes they will be the correct versions - but sometimes they won't. The only powers you have are the ones that make sense within Hex. Native AU characters start here.
2 - Something is wrong with your head. You get flashes of people and places you've never seen before. Sometimes you go to use a power and something about it seems not quite right. Maybe you're the one who's not quite right.
1 - You have the eerie feeling that you're forgetting something, all the time. When someone tells you you've lost memories, it instinctively makes sense to you - but all your memories are there, aren't they? You're not missing anything. But the nagging feeling won't go away.
0 - Lost memories? What lost memories? Characters at this point are functionally NPCs, and have no idea that they ever had lives outside of Hex. Trying to convince them otherwise just sounds like crazy talk. At this point, the stigmatic markings on PCs have disappeared, and they also cannot perceive the God-Machine and don't have any memory of having seen where the gears were in the past when they did see them.
When your character dies, please fill out the form below and leave it in a comment on this post. Note that you do not need to fill out this form for a death circumstance that does not cause a rewind of time; a Sin-Eater revived by their geist doesn't need to fill out the form (unless the player chooses the rewind instead of geist revival), though the mods would still like to know about it. Likewise, the death of a Demon's Cover isn't necessarily the death of the Demon, but it's a highly likely thing.