There are a LOT of problems for the Gov in Kiev, beyond what is going on in the Southeast.
The tires are appearing again on the Maidan, there have been clashes between the Right Sector bunch that supports the new Gov and the Maidanites, and Poroshenko is threatening to bulldoze the tent citty of the Maidanites.
Add in reports of anti-war unrest in the western part of the country, now that casualties are mounting, the Maidanites sudden turn AGAINST the EU and the proposed austerity measures, and no one except the Gov Heads getting paid in months, the place is a powderkeg.
Putin merely sees that as a bonus.