I'm having the exact same problem ever since I set mine up (finally picked it up from customs yesterday). It switches off arbitrarily and this morning I wasn't even able to turn it back on before letting it cool down for a couple of hours.
So naturally I thought it was heat related as I have my network stuff stowed away in a cabinet. So I hooked up the old router, took the almond+ out and placed it on my desk, powered on but unconnected and wifi turned off, just to see what would happen without any load or heat buildup. It stayed alive considerably longer but eventually switched itself off again, even though it hardly felt warm to the touch. A quick power cycling was able to revive it this time, however.
I'll email support as well but thought I'd let you know that you're not alone.