For much of the period following the collapse of the USSR, Moldova was governed by an elected Communist government, uniquely among post-Soviet states. What factors were at work in Moldova which led them to choose a communist government, unlike all the other former Eastern Bloc countries?
According to wikipedia article on Moldova, communist government ruled from 2001 to 2009, so I would link its election with dissatisfaction most CIS nations felt with their democratic governments, since the 90s were a time of multiple economic crises for post-Soviet states. Ruling Moldovan democratic party at the time has succumbed to internal conflict and failed to deliver on its campaign promises, thus losing trust of the people, and the communists moved in to fill the void. And since then right and centrist parties were unable to effectively consolidate until 2009, when they unsuccesfully initiated parliament crisis to depose Communist president Vladimir Voronin, but failed to capitalise on it. That crisis culminated in civil unrest, which, again, led to loss of trust by those parties.
Thus, the only reason moldovans chose this government is that they saw that communist party relatively consistently delivered on what they promised, and democrats did not. That is not to say that they chose communism - some sources view this party as communist only in name and in fact being rather centre-right.
Another point of note is that prior to 2001 election Moldovan electoral legislation changed, which also might've contributed towards communist victory in that particular election.