Why is my database becoming suspect?
Knowing that a CHECKDB returns errors right after restoring a backup, as stated by Remus Rusanu, you have a corrupted backup. As fixing this afterwards is usually much more painful then before, you should plan (or ask your DBA) to check the consistency of your databases on a very regular basis. I remember having anxious moments waiting for the results of a first DBCC CHECKDB for databases that have been in production for a few years, long before I started my job.

If you want to know more about corruption and DBCC, have a look at:


How to corrupt a database, by Kendra Little: http://www.littlekendra.com/2011/01/24/corrupthexeditor/. I found it a great way to understand how things were working under the hood.
Paul Randal's articles, for example http://www.sqlskills.com/blogs/paul/category/checkdb-from-every-angle/ . He is THE authority on DBCC and you can also subscribe to their newsletter. The last one has a great introduction video on corruption and how to fix it.


So check (sorry for this one) the health before, try to restore a valid backup, and if you have no other choice, try DBCC REPAIR_ALLOW_DATA_LOSS. But as stated before, you'll lose data and that can even make your database unusable.