Sql-server – Log Shipping always fails, after a while

I have a problem with Transaction Log Shipping on the SQL Server 2014 edition.
I have to log ship 4 databases, 2 of them are fine and the other 2 ALWAYS fail but not at first. When it fails, SQL reports that one of the log backups in the chain "could not be verified" thus breaking the chain.
These 2 databases in question will also end up in a "Restoring" state. All the articles that I have read about this issue report that I should put the database in emergency mode and run a DBCC CheckDB, but I can't since the database is in restoring state…

Additionally, I have verified that the broken log backup in question is valid by running a RESTORE with VERIFYONLY, and no errors are reported.

I have set up log shipping on these two databases up at least 7 times now, always to have it break in a few hours. What can cause this behavior?

Here are some of the logs. This first one is the last successful restore after setting log shipping up again:

2016-11-23 15:41:53.66 Restored log backup file. Secondary DB: 'XXX', File: 'XXX.trn'

And then the very next message is

2016-11-23 15:41:55.29    *** Error: Could not apply log backup file 'XXX.trn' to 
secondary database 'XXX'.(Microsoft.SqlServer.Management.LogShipping) ***
*** Error: An error occurred while processing the log for database
'text.staging.fsintel.com'.  
If possible, restore from backup. If a backup is not available, it might be necessary to rebuild the log.

Both instances are on SP2 GDR.