What happens when you restore the same transaction log multiple times?
Restoring the same transaction log over and over buys you nothing.  The changes in the log will have already been applied to the database files after the first restore and no further action is needed on subsequent restores of the same transaction log backup.

Also, keep in mind that you cannot access a database until you have issued the with recovery command UNLESS you are using a standby file which will enable read only access.

Depending on WHY you are wanting to keep in sync with your production database, it sounds like you might want to research log shipping