When is damage "permanent" in Accel World?
It seems not to be some kind of "rule", but aspect of specific stronger abilities/avatars:


it was explicitly said that Black Lotus avatar inflicts permanent damage with her blades
"steal" ability wouldn't be much of a steal without permanent aspect to it


I don't think it was explored (in anime at least) if there are ways to purposely achieve it (from leveling up would be logical) or as other aspects of avatars some people just happen to have it.