Online users' status showing as offline

I've recently upgraded OpenFire to 3.9.3 and immediately after the upgrade we began experiencing an issue where:

1. When a user logs in to their client all users show their status correctly. However, after a certain amount of time has passed users in their contact list begin to appear as offline, although they are still online and can be communicated with as normal.
2. If a user that appears to be offline changes their status then that status change is correctly reflected in the client. But again, after a certain amount of time passes that user appears to be offline again.

I've done some searching on the issue and have tried suggested fixes, eg:

1. Fired up ntpd to keep the system clock in sync.
2. Updated Java.
3. Increasing the Roster/VCard cache sizes until they are no longer being shrunk frequently.

None of these have worked, I can no longer see anything in my logs that might indicate a problem.