Reply to "Problem with my dads old train set."

12 ft spacing is more than good enough to not have the problem you are describing.  I seriously suspect there is something wrong with the locomotive.

Same questions I had before, do you have any other motorized equipment, and does the same problem happen when you run those?

Do you or can you get alligator clips? ( yes I know the center rail lead is not hooked up in this picture)

If so, turn the loco up side down on a towel or something soft, make sure it is secure.  From the transformer, clip the hot lead to a roller pickup and clip the ground lead to the metal frame.

I used blue instead black for the arrow for better contrast. 

Turn the transformer op to what you normally run at, and just let the wheels spin in the air for 15 minutes or however long it normally take for the problem to arise.  Since there's no load this is a guaranteed means to that the problem will show up, but if it does show up you can probably stop messing with the track.  As stated before if no other equipment is doing this on the track, it's likely not the track.  Another method is to set the engine up on rollers and let it run for a while. 

One caveat is I can't tell what type of reversing unit this machine has from the pictures.  From your description of a switch on the top, I surmise its an older style that tends to get gummy.  Since these are spring and gravity operated you may want to block it wood/books/etc and let the wheels face down while spinning.