Press the two halves together while trying to turn it on. If it turns on, you have the well documented press fit battery connection problem. Usually the turning-off will happen when you are riding. Initially once in a while then more often. Call Garmin. They will offer you a refurbished unit for about $100.
The problem stems from the way the unit is put together. The two halves are glued together, and there is a spring press connection to the battery that loosens over time. They corrected this problem in the Garmin 705, since the two halves are screwed together.