Questionable Questing

previous incarnation had in time, unless they actively reject that part of the memories. It's just, they won't get it any faster than in the prior life without focusing on it, and it wasn't enough for them last time. Make it less a quest about someone reclaiming a barely remembered powerset and more a quest about someone struggling to be /better/ than last time - to be good enough.

That might mean cultivating the skills they were already going to get sooner, and pushing their mastery further, or it might mean patching the holes in their proficiency that laid them low originally.

Yeah some of the most well-motivated rebirth or return-to-an-earlier-time stories I've read have started with the fact that some tragedy or disaster happened in the future and the MC couldn't prevent it the first time around.

Basically, what I'm going for in this concept builds on that - it's not 'I need to train to reclaim the power I had before', it's "My power is coming back slowly, but I can either work to reclaim it faster or cultivate additional abilities to meet the horrors head-on."

Also they might not have actually reincarnated in their own original body, but who knows.

If they aren't in their original body, that should probably be developed as a major theme. It would be kind of odd to do that and then not talk about it much. Another thought is that as soon as they start making changes, or if they are perceived as a different type of person/being, they might not get the same opportunities as the first time around, making some skills difficult to gain or explain having.

Are you doing a game interface story or one where the reset is a singular act of magic and they have only one mortal life to get it right this time?

First off, I'm not really considering writing this. I just like throwing ideas out.
Secondly, part of the premise here is that their soul bears the echoes of their past life, and as they age it will naturally carve their prior muscle memory and capabilities into them, at the same point in their life as they originally gained them.

If they train for something in particular, that can speed up the imprinting of that particular thing.
The issue is, their original death is also marked on their soul. If they can't resolve things before the time when they originally died, their particular form of extemporal reincarnation will cause them to weaken and die in short order -

and if they can reincarnate again, an early death will shorten the time available to them in all subsequent loops. Possibly cutting off their natural recovery of certain abilities if they haven't regained them at an earlier point.
If they can resolve the plot with enough time left in their life, they /might/ be able to find a way to escape the otherwise inevitable recurrence of their death.

As they age it will naturally cave their first life's abilities into them due to a soul echo... That's an interesting variation on the life redo story, haven't seen it before. Is it inspired by anything in particular? It implies an interesting concept of time; that the future exists before you get there, and the past exists even though it's apparently being rewritten.

Not based off of anything, really, but the basic idea is this: the soul accumulates a record of everything that happens to you, physically and mentally in your life.
Reincarnation is not a natural phenomena, but when it happens, someone's soul starts from the beginning

...and as it overwrites any part of itself due to reaching the right temporal point in life, not only does that part get written onto the current body, mind, etc, but it basically gets re-transcribed into the soul along with the current life.

Because this person's soul has been sent back in time, this happens to be occuring in the past.