Either the Jetpack is suffering from a temporary issue and needs to be reset at various levels or the service in your area is too poor to maintain a constant connection. The easiest way to narrow down those two options is to compare service from another VZW device from the same location. If both devices perform poorly its likely service related. If only the Jetpack performs poorly then it may be something temporary or bad hardware on the Jetpack.
Maybe I'm not reading your question correctly but if the Jetpack is turning on and off then it may also be a battery problem. In that case you should be able to leave the Jetpack connected to a wall power source and observe if there is a difference between a stable power supply and the battery. The battery of the MiFi or the contacts to the battery may be bad and need replacing.