What reasons are there for a stove's burner plug to burn out?
There is virtually nothing you could do to cause an electric element to fail.  The element is completely sealed and it plugs into a receptacle in the stove that is made to accept it.  When they do fail it is due to age and usage. They can wear out by using them.  Putting a pot on and off the burner over and over for YEARS can wear through the surface and cause a short at the burner.  YEARS LIKE 10 OR 20.  If you really meant to say "plug" then the wear and tear would happen when removing the burners to clean the drip pan. Again, over years.  You can't use a stove without this happening. Things wear out.