Are you using the serial port to communicate or the Ethernet port?
A long time ago we used L31's and PanelView Plus over serial, the early v17 firmware would behave like this. After a day or so, the comms would drop and only a reboot would cure it. Maybe the L32E's would suffer from the same firmware bug. That's probably a long shot. If you happen to be using v17, I'd make sure that it is 17.7.
If it's over Ethernet, the first place I'd go to is the web page of the L32E. There are some really helpful statistics that you can look at to help diagnose issues. I haven't looked at a L32E's web page in quite a while but something like the diagnostic overview, look for missed and rejected packets, this should be zero. Ethernet Statistics will have a bunch more statistics like FSC, alignment errors, collisions and such, again a normal system they will be zero. The other thing that you have to watch out for over Ethernet is the number of connections. If the L32E is exceeding the number of connections, that could cause your L32E to stop communicating to your PanelView.