My problem is fixed - it looks like having the correct Windows time is critical. It's because the default Windows time server could never connect to sync my time. I changed the server to time.nist.gov and modified my registry value so that it updates once per day.

I still find it hard to believe that BOINC would "trust" the client PC's clock to handle deciding when a task would be overdue - this seems like something that would be easy to do and much more reliable to keep track of on their end. Either way, it's not an issue anymore.

Thanks again for all the helpful comments.