I use the LL Official Viewer and this has always been how it works for me, it is not a new problem. I have to be online when the group invitation is sent. If I am not online, then I get the invitation, but nothing happens when I click accept.
Incidentally, friend requests work the same. If I am not online, I get the request, but clicking it does nothing.
I asked someone who uses Firestorm and they said that they don't get either of these problems, so it seems to be something with the LL Viewer.