I had silmiar symptoms listed in this thread, not starting with remote starter...sometimes, thinking there was a battery issue. I took my truck to dealer and they load checked the battery. It failed and was replaced.
After a week or so the symptoms actually got worse, clock resetting, instrutment back lite flickering, Stabili-trac going off, etc. After reading this thread I checked the battery connections and found that the postive lead coming off the battery going to the 175 Mega fuse was not tight at the fuse(located on the firewall near the battery), and I was able to wiggle it loose. As an Indusrtrial Electrician, I know the importance of tight electrical connections. This post, lug and nut did not have a lock nut on it, so I added one to keep this connection tight in the future.
Added this reply after finding this problem, and will reply again if this did not clear the isssues I was having.