Was the server downtime on the SOURCE of the logshipping or on the TARGET?
You mention the LOG backups are created correctly. Are the LOG backup files being copied correctly? Are you having problems with restoring them on the TARGET? If so: what error message is logged on the TARGET?
1> Yes server downtime was on source target while dr was not shunt down.
2> Yes log backups are created correctly.Log files are too begin copied correctly.
3>No we are not having problem on restoring it too.
But it just that log shiping reports which we use to track whether primary-DR are in sync or not is showing wrong information that log backup for xyz database hasn`t been performed for abcd mins