Welcome to AA!
I don't know quite how to say this, but it sounds like you might have a perfect storm for disaster brewing. A little more information about your setup would help a lot.
- What kind and how many fish do you have in your 20g? There aren't any goldfish that can live well in a 20g for very long. Even the little comets can get a foot long.
- What kind of filtration do you have? Goldfish are messy and need a lot of filtration to keep the water quality good.
- Do you test your water quality? If so, what are your ammonia, nitrite, and nitrate levels? If not, I highly recommend getting a good liquid test kit. I recommend the API Freshwater Master. It seems a little expensive, but it lasts forever and is vital for good aquarium health.
Now for your original question: What kind of pump are you running and how is it dying? If the motor is still running, but it's not pumping air, I'd look at your system for excess back pressure.
If the motor dies, I'd check your voltage source. My parents went through a couple routers recently and the problem was traced back to having 135 volts instead of 120 volts coming out of the wall. The power utility company had to fix it.
Cheap pumps could also be the source of your problems. I don't run an air pump on any of my tanks, but there are many people here on AA that do and could recommend a good brand of pump for you.