This isn't a good resolution, but I thought of a temporary work-around for the time being. I set up 2 "Smart Actions". The first starts at 4:59 AM (and every two hours thereafter), and ends at 5 AM (and every two hours thereafter). I had to create 12 custom time-frames for this. The "Action" is configured to turn OFF the background sync. Then, the second "Smart Action" starts at 5 AM (and every two hours thereafter), and ends at 5:01 AM (and every two hours thereafter). I had to create a second set of 12 custom time-frames for this. The second "Action" is configured to turn back ON the background sync. Without this smart action configured, I noticed that push-email sync seemed to die out after a while, even though it was always turned on. So, by bouncing the sync ever 2 hours, I'm hoping it never gets to the point where it "dies". I dont know if 2 hours is too little or too long. I was going to try every 3 hours, but figured 2 would be better. I supposed I could do every single hour if needed.
I haven't tested this completely yet. I'll go with it for a few days and keep everyone posted. The better solution long-term will be to get the push syncing issue with the Razr Maxx fixed.