Putin had plenty of chances to, yet he didn't use any of them, and I'm afraid he will not.
Though as pointed out it isn't up to just him, there is an important cautionary tale here.

In 1969, everyone (in power) wanted the Vietnam War to end. However, Nixon and Kissinger escalated military activity and at various points rejected overtures for peace from the North Vietnamese.

Why? Because they wanted to negotiate from a more advantageous strategic position at the inevitable peace conference.

What happened? In 1973, both sides came to the table with basically the same cards as in 1969 - but with hundreds of thousands more in dead.

So of course there are risks like that in international relations. But in this particular situation, there are hopefully many more factors encouraging the players to end the game (i.e. the "active" crisis), cut the losses, and plan for future strategic maneuvers (i.e. economic, political, and, yes, military development and policy tweaking).