It's a drywell... water goes in and is absorbed into the soil. If you are in an area with sandy soil, this is usually ok. In heavy rain seasons, the water table rises as more and more water is absorbed into the ground. As things return to normal, the water table drops.
If you're interested, Google for "water budget" or "groundwater budget" and you should find some more detailed explanations.
I'd recommend monitoring the situation. If it seems damp often, start to do what you can to direct stormwater away from the house. Put extensions on gutters and regrade around the perimeter of the house.
Obviously, the soil needs to be graded away from the house (in the back yard). If that means you need a retaining wall, then you need a retaining wall.
Regarding the swale, improved drainage sounds helpful. The real question is, why isn't water shedding (what is the real issue)? I've had swale issues, and the problem in those cases, was not with my swale, but the neighbors'... so water backed up in my yard. In such a circumstance, you can talk to the neighbors about the issue, ask them to fix it, offer to help, and/or sue them for damages.
But if the neighbors aren't to be blamed, then another alternative to keep the grass cut very short (grass slows drainage). Or you could check into a trench drain (concrete ditch). This is just another option that I didn't see mentioned, although it may not be your best option. As Tester101 pointed out, being there to see the issue is probably necessary.
Regarding power outages, gasoline or propane generators are the most reliable answer. A moderate generator should be enough for a sump pump, the fridge, and should keep the toilet flushing too. As you know, the drawback with a battery bank is that once it discharges, then you don't have a simple solution, like getting more gas.
Edit- Here's a possible way to use a retaining wall to increase the grade away from the house.
Best Answer
If you have to pump you want to get the water away from the home so use smooth wall it will drain easier. In a trench you would want to be below the frost level. Make sure to extend the drain far enough away or down hill or your power company will start sending you Christmas’s cards (joke for high use electric homes).