What causes the threads on bike pedals to become stripped? Is there something I can do to prevent my bike pedals from wearing out? And what causes the threads on a bike pedal to wear out? 

I have a 4 year old Raleigh road bike with just regular open pedals. After 300 miles of riding, I had to replace the pedals because one of them broke off when the threads on the arm that the pedal screws into wore out.  

The bike repairman offered to send the pedal out to be re-threaded but that would have taken a week and cost more than just replacing the pedals.

Any suggestions or recommendations?
It probably means that the pedal was never installed correctly: either it was not tightened enough or it was cross-threaded.

It's actually not that hard to install a pedal incorrectly. If you miss perfectly aligning the threads, it's called cross threading. It's possible to cross thread the pedals and still have them feel like the pedal look like it is installed properly.

However, if you look closely, you'd see that the pedal isn't perfectly perpendicular to the crank. When you pedal, you'll feel a pop as the pedal goes around when your foot crests and the pedal (due to not being parallel to the crank) has to change orientation.

Over time movements of the pedal relative to the crank will slowly strip out the threads on the crank, on the pedal, or both.

I could speculate that your raleigh may have been purchased at a department store, and that it wasn't assembled by a professional. They didn't install the pedal correctly.