Offline Files Notification, still connected?

Recently in my office, we have had a few employees who have had some odd experiences. While working, they will receive notification that they are no longer connected to the network drives, and thus unable to synchronize, yet they never actually lose network connectivity. They can instantly synchronize and it works. However, since their .pst files are located on the network, they end up having to restart their computers. Since they never actually disconnect, and their email is affected, I have no idea what to do now.

I have tried everything I can think of. Anybody have any ideas?

Also, if you need more information, please ask. I will do what I can to communicate the problem, steps, and hopefully solution!