I had this happen to me this morning and I fixed it doing a few things.

1. switched recovery mode to SIMPLE from FULL and FULL to SIMPLE to break the backup chain.

2. took a full backup of all databases using the maint plan.

3. took trans log backup of all databases using the maint plan.

This fixed the first node. I am in an AlwaysOn configuration so I had to remove the databaes form the AG group and put them back when I was done. Here is where it got crazy.

I went to the second node and ran a full backup using the maint plan, worked, then I ran the trans log backup, it failed. HHMM...

I looked at the history of the main job for my trans logs, I saw this error number -1073548784. Couldn't find anything on it. Then I thought I am going to script it out to see what is going on and where it is failing. My user databases were getting backups but not my system from the execution results running it as a query. I then went back into the main plan, said only backup tran logs for user databases. The maint. plan finished with success. I then went and maunally did a full backup on my systems databases, Master, Model, MSDB. Change my maint. plan back to backup all databases, ignore offlines and ran it again. it FINISHED WITH SUCCESS.

Hope this helps someone! 🙂