Hall of Mirrors (1953)
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The current year is 4154.You could further improve on the initiation process to reduce that time, and just have more frequent revisions.
So I wouldn't expect the guy would have to be returned to the same state every time repeatedly, as the tech is described.
The point of my little twist is partly that: that at least the previous "self" has decided to use the machine that way, even if the possibility of doing what you say, in theory, exists.
It could have been simple human error, or the machine might be stuck somehow, but the story works better if it's a purposeful decision. Either the previous self wanted to delete their 2004-onwards memory on purpose, or they needed to restore their body to a pre-2004 state. Both of the alternatives suggest that something very bad has happened, or has been happening from 2004 to 4154.
My favorite one: he's in a bunker during a nuclear winter. There's no food and no water, but the machine has its own energy generator. He has to regenerate every couple days just to stay alive, and has been doing it for 2000 years. Being able to forget his situation is what makes it bearable.
Maybe preserving some of that memory, without preserving so much it becomes too devastating?