Missing data in specific tables post log backup and shrink
We have two DB servers which are part of Always On. Recently we noticed that log backups haven't been running on them for sometime and their ldf files were growing. We took a log backup and tried to shrink the log file. Not sure if the shrink actually ran, the wizard closed in 2-3 secs and the ldf file size didn't reduce.


Did you check that if both of the AlwaysOn servers are in a healthy state? It seems that the log backup is not happening because the principal logs were still holding up, which could be due to the following reasons:


the secondary server is down
OR; the databases are not in a healthy state
the redo logs are applying very slowly on  the secondary server


Look into the SQL error logs as well as sometimes log backup does not work because the disk is full, and it couldn't write to it. 

If log usage is still high, you may remove the affected databases from the AlwaysOn availability group first. Wait till the log usage drop, and  then add back the affected databases into the availability group. This shouldn't cause to any impact. 


  Please clarify if the log backup and shrink has any part to play in this? If yes, how could this have been avoided and what else was supposed to be done to keep the ldf in check? 


No, the log backup nor the shrinking shouldn't cause to the lost of data. 

Have you checked if...


any scheduled job to purge away some data?
application team or the DBA who purge the data?