Just to set the record straight, "resetting" worked initially with my 4g, but only once. After that, I could hold both buttons down for 30 seconds or more and nothing! What was interesting is that several times after trying to reset the phone, I would press the "on" button and the phone would miraculously come to life. However, that stopped working after a little while.
The last time that the phone turned on was when I tried a "recovery". I had given up on the recovery because the progress bar remained completely unfilled after several hours, so I disconnected it and suddenly the phone came on. I backed it up as soon as this happened and was getting ready to try to reinstall the operating system but the phone shut down and I could never get it started again.
As mentioned above, I now have a new 5c (because I could get it for free) and I have stayed with the 7.0.2 operating system. I have NO intention of risking the upgrade to 7.0.4.
I have also managed to extend the battery life by making all of the changes recommended in the Battery Life Pro app listed under "tips". By making these changes, I went through the entire day with minimal battery draw down (about 25%). Please note that I am not a big app user and so I typically don't use up a lot of battery life unless I am on a long call. However, the first day I had the 5c and before I changed the settings to extend the battery life, I had gone through almost 50% of the battery life in about 2 hours and I hadn't done anything!
I am NOT sure that the battery life changes I made will help people with 7.0.4 that are experiencing shutdowns. It might, but in my layman's opinion, I think there is something in 7.0.4 that is causing the shutdowns. The big question I have is why is this happening to some phones and not others?