r u running ur log shipping 24 hours??
u can skip for 5-6 hours everyday and during that time you can run this reindexing job..
Mine works like this only and it is running fine !!
That's some brave advice to just toss out there without knowing more about the environment. If you have a database that experiences even a moderate amount of transactions, you could have a real mess on your hands by shutting log shipping off for 5-6 hours. Besides, if you are using LS for DR then shutting your LS job off for 5-6 hours is a bad idea, as you'd have to wait for the LS db to process 6 hours worth of txns before data is available.
What's confusing is (at least in 2008... could be different in 2005), if the LS db goes out of sync, yes the alert job barks about it being out of sync but the log shipping restore job should eventually catch back up with the primary server.
My advice is to pay more attention to what you are reindexing and why (a reorg may be more appropriate), and address that first and foremost. Then, address the duration settings on the log shipping job to possibly have the job execute more frequently, and hence less work each time. Then, wade through your error logs and possibly post back if you see that your log shipping database goes out of sync and STAYS out of sync.