My Time Machine backup says no backups for more than 2 months. Help!

Same problem. iMac 2017. We have two in the house, one fails in TM, one does not. "Show Time Machine" does not fix, I already tried that before as well. Apparently this is an Apple Monterey problem. I deleted my old backup, started a new one -- same problem. I probably should not have deleted the old one; it was probably good.

Any word from Apple how to fix?

I've been chasing this problem along with a thousand other users I'm seeing having 'no first backup' time machine problems. I saw a suggestion of excluding /Library and ~/Library. This seemed very unlikely, but I tried it and my backups are now working nicely. I can't guarantee that this was the thing that fixed it, but it's the last change I made before Time Machine started behaving. This is on new M1 MBP systems from late 2021. One system backed up fine, the other wouldn't, both setup the same way and using the same Synology DS720+ NAS. Good luck. There are a lot of reports that this problem seems to be a Monterey issue.

If you have "Show Time Machine in menu bar enabled, select it and choose backup now. Does that work?

Also, check to make sure you have Back Up Automatically checked in Time Machine preferences.