Is the Created/modified date of the TUF file same as or close to your last LOG file? ( the TUF file should be in your logcopy folder by default)
If not, very likely the Restore Job just ran its steps but didn't do any restore. In that case, you would need to manually restore the Logs starting from the earliest missing one.
To see what the last restored is, you can run
SELECT last_loaded_filename, last_loaded_last_updated
FROM msdb.dbo.log_shipping_secondaries