The frequent rain in May exposed many places where important drain lines were either not working or working very slowly. We tried using a drain auger but that either didn't work or made only small improvements. Once we found a restriction, we marked the spot for repair. Once the ground firmed up a bit, we were able to fix the drains. As we suspected, the problem was mostly roots.
I can see why this drain wasn't working well:
Thanks to a backhoe borrowed from Parks Department, we were able to fix them all fairly quickly and replace those sections with PVC pipe that is unlikely to be clogged with roots. The older sections uphill of them might be blocked, but these sections should be fine for a long time. It is never fun to fix an area and then have to re-fix it 2 or 3 years later. Roots are relentless!
We fixed 5 drains around the course ranging from 20 feet to 5 feet in length. They are mostly in out of the way locations:
These repairs will be most obvious the next time we have excessive amounts of rain. The water should have an easier time draining to a lower area instead of forming a temporary pond.