Ukraine

On a strategic level it will be hard to not take it back. This makes Putin and Russia look extremely weak. The longer it takes Putin to take back that territory, the weaker he looks. This matters a lot. First of all a number of countries have withhold weapons to Ukraine, due to fear of escalation. If Putin can not do it, then that fear is gone. Even more important is Putin's support within Russia. If Putin looks weak, then somebody else might have some ideas about getting rid of him. That is a problem. Also public support is very likely taking a massive hit. Even if it does not lead to a revolution, it does bind armed forces needed to oppress the potential opposition. Those men are then unable to fight. Then you have other countries looking at the weakness of Russia and the opportunity that gives them. Belarus army just had to hand over a lot of weapons to Russia and I bet the Russian soldiers in Belarus are not armed very well. So just a imagine a revolution. Especially with a bunch of battle hardened Belorussians, who have thought in and for Ukraine. Georgia is another country looking at this. The current government is loyal to Putin, but they have an election coming up. There is a strong possibility that Georgians kick them out.

As for the tactical level, Russia has to move quickly as Ukraine is building defenses. It is much easier to take back land in Kursk then further south.