In the Login properties of one of our reports in the User Mapping page we have a user called copump. Every couple of days, the db_datareader role turns off. What can I do to keep this account from losing membership in theis role?

Do you have Scheuled restore of the database from any other environment..

 Not that I am aware of. Wouldn't that erase any data input into the database? How can I check that?

Check the system table restorehistory on msdb database

 Is there anyway to lock that role to keep it from being removed regardless of restoring?

No, you can't...You shd add the user after each restore

 It isn't a restore, is there some way I can audit what is making the changes?