Log Shipping "out of sync" but none of the jobs are failing
Well it didn't fixed. I think I will recreate the log shipping again


Before , you give a try with that, why don't you go for looking the most recent differential backup and restore it on the secondary.

We also had situations as mentioned above and found that:

This happened due to NW glitch due to which the folder shared(on primary as common backup location with secondary) was no more shared ( due to some issues on cluster resource) and as a result few log backups never went/copied to secondary and since there was a gap, even though restore job completed but LS kept saying out of sync.

Well, in our case we went ahead and restored the latest full back up to bring the missing LSN chains in sync and later the restore job picked the next log backup file and LS was back in sync.