I checked a Facebook group I am in. Three recent (within the past six months) pieces of info. 1) One may not enter Abkhazia from Georgia at this time. 2) One may enter Abkhazia from Georgia if one has advance permission from Abkhazia (no mention of how to obtain the permission). 3) In any case, if one exits Abkhazia via Russia, one will not be allowed to enter Georgia ever again (I assume on the same passport).