Log shipping 2008 r2 SP2 server to a 2008 r2 SP3 CLUSTER
Logshipping is a death tested technique that has been around since many ages. 

Looking at your specific error sequence on secondary server


The log restores errors out after a couple of successful restores.
The database goes into suspect mode
you tried to restore the log files and they restore it fine, so the log files are not corrupt.


You should check if the Bytes per Physical Sector on secondary server for the disk that you are trying to restore is NOT 512 bytes.

You can install the Hotfix for SQL Server 2008 R2 SP2 or correct the disk bytes per physical sector.