However, I am finding I'm unable to keep Minepeon running for more than 24 hours at a time. I'm not sure where the problem is yet. I'm going to have to hook up a keyboard so I can see what's going on.
Have you checked if you donate Mining Time in Minepeon? If so, Minepeon will never run more than 24 hours until rebooting the Miner to switch to the donation pool and then back to your pool