Hi Homerj,
It sounds like their is some corruption in the project. Are there attachments in the tests that could be causing issues when they are opened and does it only happen in the test cases or does it happen in other modules too?
Have you run a verification on the project (it is non-invasive and can be run with the project active, but only the verification, All other maintenance functions would require the project to be deactivated and we would recommend a back up of the project repository and DB schema before doing anything other than the verification)?
If there is issues this should resolve them and correct the issue. You may need to remove some of the affected users and re add them back after issues are resolved as I have experienced this in the past.
I hope his helps. If the issue isn't resolved I would suggest you open a support ticket with your support group to address the issue further.
Dan