Sound like your pump isn't high enough capacity to keep up. I made my sump-setup and used a 5-gallon bucket. It will drain the bucket in about 3-seconds. Another thought is you don't have a drain backflow valve. If the pump shuts off and too much water drains back down into the pit it will make it run again. Viscious cycle.
A good quality sump-pump will not fail often at all even running constantly. Goulds is a excellent brand. The off-brands carried by lowes, home depot etc. aren't built for constant use. Buying a good quality unit is better than having a back-up unit. As for electricity loss-they make battery back-ups for the sump pumps. Wouldn't run it all day long, but I can't imagine you pump should run that much. I think if you fix the capacity problems and get a battery back-up you should be fine.