Why is the 2013 ford explorer key fob not working?

While there are a number of reasons that the key fob for a 2013 Ford Explorer will fail to work, the most common is a dead fob battery. Other causes run the gamut, from a failed transponder key, a defective receiver, or a key that somehow got unpaired to the vehicle. Another consideration is wavelength interference, especially if the failure is intermittent and location dependent. The first thing You should do is to see if the doors will open with a spare key fob, if You have one. If You do not -- or if the spare key works -- You should next try replacing the battery in the failed key fob. These are CR2032 button cell batteries, which can be had for a few dollars at most. It's worth a try before You delve into more costly repairs.