It gets like 170 hours of standby battery life or something according to the manual, so that's like what, almost a week? I haven't had mine die yet and I've left it plugged in constantly, always on. It charges while I drive, and my power port stays on for about ~30 minutes after I turn my truck off so it charges then too.
I can really only see it dying completely if I went on a trip for a week or something and did not drive my truck. I'm not sure if it would come back on instantly if the battery was dead and it suddenly got power, but If I had to guess I would say it would.
So it works great for a permanent install