No. It's much worse than that. It doesn't remember what it just said the message before.
The thing I don't understand about it is that it works pretty great for a while but, eventually, it starts acting erratically, forgetting things it knew, not following instructions, etc. It's not that it forgets old things or can't learn new things, it just becomes dumb.
Maybe that's what you're talking about but I don't think AGI is going to have the memory of a goldfish.