This is isn't fixing the issue, but just explaining what is going on. The reason when you hit the button to turn the heated steering wheel on and it goes out after a few seconds is that the ECM is detecting either an open circuit or a short. Either case it knows something is wrong and turns off the power going through the circuit. The open circuit is just like it sounds, like it is unplugged. Anything from a loose fuse, loose connectiong/unplugged (including at the clock spring), broken wire harness, or even a break in the steering wheel heating element. The short means the power wire is grounding out. For example the 12v power wire is broke and exposed, and touching some other metal surface. Often the ECM (or BCM maybe in this case) can detect that and shuts down the power before it blows a fuse or burns up the wiring.
Intermittent electrical issues like this are extremely hard to track down and fix. If the issue isn't occurring right at the moment there is no way to verify what is causing the issue. In this case the only option is throwing parts at it and hope you get lucky, and not way to verify you actually fixed it at that time. Obviously you can do a visual inspection, verify the fuses are seated, and double-check the connections are tight. Then it's just a waiting game to see if the issue comes back....and always the question of whether the issue came back because it wasn't truly fixed to begin with, or there is a new reason for it!
