How would I go about tracking this issue down?

One of my websites has been up for years without issue. We're using Godaddy's nameservers for our domain.

Lately in the past two weeks, I've noticed that once from home on my Cox cable connection, I could not connect to the site... it said the domain could not be resolved. I checked downforeveryoneorjustme.com, and it said it was fine. The "outage" lasted maybe five minutes (through a reboot too, and I'm on a mac FWIW) and then it started working again.

Then it happened again this week, but from our office on a different Cox connection. Then it happened again from the office, but for a different domain. I called Cox during one outage, and the tech there could resolve the domain without a problem.

When these outages are occurring, I can issue "host mydomain.com" and get "domain not found", but using "host mydomain.com 8.8.8.8" will resolve normally.

Where do I start? We're getting reports now that our customers are experiencing it too.