@Texas Dale, I have a hunch it is the wiring too. Yes LEDís do fail but I bet the total hours on your trailer LEDís are minuscule compared to the ones you replace on your house.
Also, keep in mind all the trailer wiring and every connection, splice, housing, etc. spends a bunch of time vibrating and bouncing down the road.
My two cents is you should take a good look at the wiring back there and also check with a multi meter if possible to make sure you have power to all of them. You could also swap a good and bad light and see if the good one stops working or not and if the bad one starts working. No fancy testing equipment needed for that.