There are some reports that as we get closer to the end of the semester, SafeAssign is slowing down because of increased submission of papers. If you have given your students SafeAssignments, it might be a good idea to tell them not to wait until the last minute to submit them.
Another suggestion is to not have assignments or tests due on Sunday nights. The reason is that most students will wait until the last minute to do their assignments or take their tests. However, at 10 pm on a Sunday night there is no help available if they need it. Most likely you don't want to have to answer frantic student emails on Sunday nights either.
Try making your assignments due during the day on Monday. That way the Help Desk is there to help them and you if anything goes wrong with Blackboard or the network.