While perusing TV Tropes, I came across the following description of a story/book involving mental time travel. Unfortunately, Google provides no hits when searching for its title, so I'm guessing it's not in English, though I could obviously be wrong. Here's the summary:

In "Cube with Faceted Edges", this is the only possible method of Time Travel. Originally used exclusively by the special forces-like Harders with brain implants called Iscapes, which throw their consciousness back a few seconds at the moment of death (how death is determined is not clear). To an outsider, it looks like a Harder is impossible to kill, as they look like they can dodge bullets and have a sixth sense. In reality, the Harders are just using the foreknowledge to avoid the same deadly outcome. Later on, a rival organization obtains an Iscape and builds a similar-functioning device that works by thinking of the time you want to go back to. This is one-way, however, as the timeline is changed by this action. They then start selling the devices to the general public and eliminating anyone who tries to investigate them (easy when you can always go back to fix a mistake). The knowledge of the original timeline quickly fades if any changes are made.

The protagonist (a Harder) starts suspecting the existence of these bootleg devices when a space liner explodes. While it looks like a typical malfunction (and it is), he does find it strange that a full third of the passengers have cancelled their tickets several days before boarding. It turns out they all have these devices.

He also finds out that a Harder was on the same flight but managed to survive. The Harder reveals that he spent countless iterations trying to stop the explosion. Eventually, though, his traumatized mind forced him to board an Escape Pod moments before the explosion. He ends up having his Iscape removed and committing suicide.

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    No ISFDB entry, so this work was probably not in English. The entry was added by ChronoLegion, someone who is known on TVTropes could try contacting hir. – user56 May 11 '14 at 20:27
  • It could also be something like fan fiction, or an unpublished short story by whoever made the entry. TV Tropes has no notability requirements. – John Meacham Jul 19 '14 at 1:46

Google search offered me this page while I was searching for the same book, so I’ll answer the question in case someone else wanders here later.

OP probably couldn’t find the book because it’s a Russian work—it’s “Cube with Blurred Edges” («Куб со стертыми гранями») by Vladimir Ilyin (Владимир Леонидович Ильин).

You can download it here.

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    You have my +1. Let's hope the OP sees this :-) – Valorum Oct 25 '14 at 19:44

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