It sounds great to go mountain biking! Plus it's very smart to have a phone with you for emergencies! What you describe sounds as if you are not getting a good signal, most likely due to the terrain. Does your phone show "Searching for service" or a low signal when in this area? If so, I would recommend leaving the phone powered off when not in use. If searching for a signal, the battey can drain quickly. Do you notice the same thing happening in other areas, or in the location where you go biking? Please let me know some additional details, thanks!
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Sometimes, when rebooting the phone, it's typical to see some battery drop (or, when charging, an unusual jump in battery). I think this has something to do with how the percentages are reported. When the phone is completely off for along period however, There should not be this much of a drop. It sounds as though you either have a bad battery (some Rezounds were shipped with defective batteries, usually evidenced by running hot) or possibly a short within the phone. You may want to take it either to a store or call tech support. Get one replaced, then test it. If you still have a problem, get the other replaced.
I have seen on my Tbolt a 10-15% drop on battery level after a reboot. I never seen the battery drain to almost dead after being turned off for a few hours.