How do I stop the power adapter in my computer from dying?

if the power supply keeps failing the first thing I would check is the receptacle that you are pluging into. There should be a good 120 volt power source to begin with. Use a meter to check this. If the power source is working good and is uninterrupted the problem would seem to be the computer its self. Maybe the power supply is not big enough to power all of your computer inner components and is failing due to its size. Maybe the ventilation is not adequate to cool the power supply, bigger cooling fan is needed. This should not continue to be a problem if the computer is set up right other wise the cost of repairs outways the investment of a more dependable computer. Your time and frustration should be taken in to account if you choose to keep replacing parts.

Buy an UPS ——> http://en.wikipedia.org/wiki/Uninterruptible_power_supply