Full membership does not by itself extend registration of countries. You need to spend the GC (either through direct 30-day extensions, or boosters) to extend registration of your nation.
I personally recommend buying boosters, as keeping a country costs 1 GC/day regardless of whether extended by booster or membership screen. Boosters, however, give you some ingame benefit (even if minor) whereas extending through the membership details screen provides no ingame benefit.