I've been reading a bit about the fairly peaceful transition of power in Czechoslovokia through the protests throughout the country, but I'm wondering, why didn't the ruling party attempt to bring the military to the streets to shut down the protesters with force?
Communism has always been buttressed by force.
In Eastern Europe it was either actual Soviet troops (Germany-1953, Hungary-1956, Czechoslovakia-1968) or the imminent credible threat thereof (Poland-1980). Local troops has never been particularly reliable.
You need to look at the context. Communism was crumbling everywhere. By 1989, Gorbachev made it clear that USSR will not intervene, and it was perfectly clear that the communist power could not be kept. The choice was not "keep power by force" vs "relinquish power" but "relinquish power peacefully" or "be forced out".