Do heavy human losses put pressure on an autocratic leader like Putin?

In democratic countries, there tends to be great aversion to loss of life from military operations, and there are checks and balances that ensure a displeased populace has some capacity to vote in other candidates.

Former Australian Army General, Mick Ryan, says:

(Putin)'s certainly going to come under increased domestic pressure. He didn't level with the Russian people before this war and is still trying to hide many aspects of it from his own people.

But he will not be able to hide the increasing number of coffins from the young soldiers that will be coming home in their hundreds or thousands; that will put huge pressure on Putin.

Every autocrat has to look over his shoulder ... the pressure he will get from the Russian people, and indeed, from people in senior military and government positions, he will have to respond to that in some way.

From my limited historical knowledge of Putin and other autocrats, they do not seem to be affected by vast maltreatment of their citizenry, including causing high rates of unjustified deaths.

It therefore raises the question: do high human losses in war actually affect the job security of the head of state of an autocracy like Russia?