Absolute monarchs (or dictators) fight on long after it is clear all will be lost if they fight to the bitter end. As long as Putin can put up the appearance of being able to fight on, he will.
If deposed while still alive, where would he go? China? North Korea? Cuba? Maybe he has enough to fortify his palatial estate near Sochi for a while, but that is still within Russia, and must be resupplied with food, water, arms and energy. The big difference is that Russia is under no external threat. No one wants to occupy and feed such a vast country. So, I think that Putin can and will hold on for much longer than a year. The only thing that could save Russia now would be a mutiny from within. As we saw with Prigozhin, Putin is smart enough to smell dissent in the ranks from far off, and, as a product of the KGB, knows how to deal with it. Any internal attempt to save Russia from itself is a suicide mission. No one wants to end up like von Stauffenberg. Even if you know your ship is going down, there is always hope for a place on the lifeboats.