I've been using the stem mount on my GT Karakoram 29'er and never had a problem. If I'm going out for what I expect will be a hard ride I just double check the bands. I live in Texas and the heat takes its toll on those. I've never had the Edge come off in 3 years of riding trails.
Since I have a bike with a very short stem, I will probably have to mount the Edge on my handlebar which is tapered. There is only a very short - about 10-15 mm (a half of an inch or less) - non-tapered space near the stem. I will have to use the flush out-front mount and I am not sure if it fits there. There is also an optional mountain bike mount (010-12563-02). I do not know how to mount my future Edge 1030.
I ride gravel and off road on a rigid bike, and my out the front mount is absolutely rock solid. I'm much more worried about smacking it on a tree than I am it coming loose or ejecting the GPS. I haven't used the rubber band mount though.
Garmin do a mountain bike mount see https://buy.garmin.com/en-US/US/p/596570 It is designed to position the Edge above the stem, so is good for bikes with short stems.
When I got my 1030, I started using it for all my rides on my bikes but quickly stopped using the bands as I could easily dislodge the unit in most crashes, and even with limbs flying around the place on aggressive rides. I went back to the Fenix for aggressive rides, and use a hinged stem mount when I'm not being too crazy. I also have a 40mm riser bar that provides lots of protection in a fall which gives me a bit of peace of mind given I tend to crash a bit.