SQL Server process suspended while executing simple SQL (one row deletes and selects)
Even though you're deleting one row, do you know the code that is being executed?  Could still be locking the tables you are deleting from.  Triggers that contain other triggers are notorious for this.  

Cursors go row by row but they will put locks as well I believe so it might mean that tweaking the code is in order so that it's more set-based deletes and not row-based.