TJ- if you are able to reset the process and it works for a couple of minutes and then stops, it seems logical that it might be some type of connection to something is going out, such as the heating element. As it heats up and reaches a point, the element simply can't do get hotter and stops. Or a connection is failing for a similar reason, but that might actually be a little more concerning if a connection is heating up. Here's a video and at about 9:40 it talks about the heating element and where to find it. I imagine you could take a multi-meter to the connections to see what's going on with it.
I had an issue with my water heater recently (no the same as you) but the electric switch shorted out and slightly melted (danger, I know) but I attributed it to checking the hot water valve on the tank and it splashed up and seeped in and crated the short. looking at where the element is on these heaters, it's plausible that something similiar happened to you.