Have you repaired your permissions? This can be a very frustrating situation which I encountred after a logic board replacement.
What I did was start a TM backup, but excluded items too make it a minimal backup. Make sure you select verify in the TM option before you backup. After the current backup I was able to see the sparse bundle and the prior backups in the Finder. (Check and see after this backup if your oldest and current backups are llisted. If not read on) However, it would not remain seen in the Finder after I closed it. Somehow I was able to see my prior backups again in the Finder. This time I deleted the current TM App in the applications and copied the old one from the TM. It now shows me both old and current backups for selection.
I do not profess to be an expert on the TM. This is just how I accidentally solved my problem.
I wish Apple or a Apple Developer would make an App for these problems. Someone could make a lot a money.