My mom bought me and my sister a V4 tamagotchi and when I started I liked it. But then I tried to connect with my sister's tamagochi and mine wouldn't connect!
Plus it had scratches all over. I just tried to play with it and the battery went out!
Scratches? Was this before you bought it? Was the packaging open? If not in either case sounds like a lot of rough play in a minimal amount of time.
Anyway I agree with Mame, your battery could just be garbage. Get a new one