Well, from the Wiki: "a militia composed of ethnic Georgians who lived in Abkhazia and Russian-backed separatist forces".
Sure, there may be a slice of population that wants to leave but how can that be gouged properly when Russia keeps influencing the people and supplying weapons to separatists? There's a cause and effect here.
The fact is that Abkhazians haven't been fans of the idea of being part of Georgia, even before they were forcibly incorporated into Georgia by the Soviets, and the ethnic strife started before the collapse of the SU, and before the armed conflict (and Russian military assistance) has started. In Spain's Catalonia separatist sentiment can be gauged properly, but does that help with an actual realization of that sentiment? Not much. And that's a highly developed European country, from which Georgia is still very far institutionally, and was even farther in the 90ies.
Sure, there may be a slice of population that wants to leave but how can that be gouged properly when Russia keeps influencing the people and supplying weapons to separatists? There's a cause and effect here.