Yes, it does, unless you reset the Tama for whatever reason. Note: V2 ONLY!! If it's V1, then no, you start over. Oh, and you're welcome for the avatar! Sorry it came out a little fuzzy...
Yeah I like that a lot and wish it was on V1 because I started getting tired of having to connect the tamagotchis over and over again waiting for a present then waiting for the right present. The V2 is SOOOO much better then the V1.