That chauvanism makes a lot of sense, that it is unacceptable to admit even a stalemate versus a presumed "little brother" inferior race. But - what are your options? Are they willing to lose ALL face AND remaining military might in an actual, sustainted battle with NATO? With what objective? To get your ass kicked just enough to say that it's okay you lost to the full weight of NATO, versus admitting you put your dick in a woodchipper in Ukraine?
The thing they're actually best at is corrosive lies. Lies are the very language of Russia - if they stopped fighting today and simply claimed glorious triumph over the combined forces of NATO, the population would on the whole accept it and be thankful the whole damn thing is if not over - at least paused. I don't think it suits them to ACTUALLY fight NATO, if all you're looking to gain is an excuse for losing.
So - why keep fighting? , other than the old chestnut of sunk cost fallacy. No wars are infinite, especially at this intensity in terms of resource and human life consumtpion. Russia seems to figure there is still something to gain from slugging on. Whatever that is, who knows. They're putting a LOOOOOOOOT of resources into fueling right wing populists across the globe and it does appear to be working well enough to continue. Whether that matters on the battlefield of Ukraine in a time scale that aligns with Putin's remaining life span is a whole other question.
What I'd close with re: "why keep fighting" is this: Russia knows that their campaign of terror bombing civilians and pushing small infiltration teams forward isn't a great long term strategy for territorial occupation. Pootz said recently "wherever we put a russian boot is OURS!". That is a childish and absurd thing to say, but - he is a big boy who said it for a reason. In that clumsy attempt to redfine what it takes to legitimize spoils of war, it maybe reveals that they know that their current strategy does not achieve their objectives. Fine - you can push small groups of men into farm fields and abandoned villages very slowly. But what good is that if Ukraine can almost certainly kill them all EVENTUALLY with drones, artillery, snipers, etc. Infiltration isn't a great occupation strategy.
So - keep fighting, until....something else happens. That's always been the russian way. Keep dying, in massive numbers, until something else happens. The problem with their history is that that 'something' is often a revolution that overthrows the current government.