Sledge Hammer

Perhaps the reason Russia didn't persist in their August War all the way to Tbilisi was because they lunged blind into Georgia and after getting a bloody nose, were too confused about the situation they faced to continue deeper into Georgia:

More information is coming out of Russia describing the problems troops encountered when they invaded Georgia last month. It turns out that the Russians lost eight aircraft (four Su-25s, two Su-24s, one Tu-22 and one Mi-24 helicopter.) The Russian pilots were not prepared to deal with the three batteries of SA-11 anti-aircraft missile systems the Georgians had bought from Ukraine last year.

The Russians also found their GPS system did not cover Georgia:

Aircraft and ground forces got lost, and that led to more losses. The GLONASS problems also prevented use of Russian smart bombs with much effectiveness.

The Russians may not have had enough troops to just press on in a frontal assault after their initial losses.