By what mechanism?
Putin is up for re-election in March 2024. Presidential term limits may have been removed in 2020, but he still needs to go back to the polls. If he cannot be sure of a resounding victory, there's a good chance he will retire rather than seek re-election. He may try to declare martial law and suspend the constitution, but his political capital to do that is a lot more meagre than it was in February 2022. More than any other election since he was first elected in 2000, he will need real support from his political base, and I'm no longer convinced he will get it.
Prigozhin is now in a pretty good position to be kingmaker, even if he won't or can't be a presidential candidate himself.
Of course everyone with any loyalty to the state, or with any future political ambitions of their own has come out in support - at least publicly - of the status quo. To do otherwise would be political suicide. But that doesn't mean they actually support Putin privately.
I think any serious presidential competitor has yet to emerge - none of the Communist candidates, or Navalny, are credible IMO. 9 months is plenty of time to make a campaign happen though.
It's at least as likely that, off the back of the poor performance in the war, and especially the dismal reaction to the Wagner affair, that Putin will be simply "encouraged" behind the scenes to retire rather than run again, and United Russia will put forward some kind of "interim" candidate who will probably win.
FWIW if you want examples of leadership changes during a war, how about Neville Chamberlain? Or the two revolutions in Russia itself in 1917?