Welcome to the forum, Apple,
Can you confirm the version you're using? - sounds like pre-7.
I had a similar problem years ago, but it was because I hadn't realised that I could only make changes whenever I highlighted the Group. I found it misleading because I could click on the other columns in the access table and apparently change things, and I seemed to be able to make changes but then they just didn't stick.
I accept that you say you are 'clicking on the Group', but your problem sounds very similar to the misunderstanding I had.