The main issue is that if the Russians are forced to abandon all of their gains on the Izyum front, they will in all likelihood need to mobilise in order to retake them. They have been waging a slow, methodical campaign, relying on a small, professional force - it looks very unlikely that they will be able to regain everything with their numerically inferior force in any good time frame, if at all. They will need to mobilise, and that seems to be something Putin simply does not want to do.