Upgrade/replace the power supply.
After having the same problem with Line 6 Pod Go turning off and going to whitescreen, and searching the Internet forums, I notice the transformer in the original power supply was moving around in the case. The Line 6 Pod Go would make a pop sound after 30 minutes of continuous play, then blank out. After replacing with an upgraded power supply per spec ($22 Ablegrid on Ebay), haven't had the dead screen at start up or the device freezing up during session.
You're welcome.
