The latest version of Lemur seems to be more stable than earlier versions. Make sure you are using the latest version on both machines (computer and iPad).
Perhaps this is another symptom of a problem USB cable ... I see many threads about problems with AxeII firmware updates that are eventually solved by swapping the USB cable. I've noticed the Lemur Daemon will not always auto-connect to a external MIDI device if the device is unplugged and then re-connected. If the cable or connecter loses connection even for a split second, the Lemur Daemon might not recover, and you would see this as a dropped connection.
Try a different USB cable. Use a short USB cable is possible rather than a long one. Try inserting a USB hub between the computer and AxeFX. If you have neighbors who have WiFi routers, your WiFi bandwidth might be improved by switching to a WiFi channel that is not being used by the neighbors.
What is your setup? (Mac or PC, operating system, iPad IOS version, iPad version?)