HiCustomer Thank you for asking your question on JustAnswer.
There are a couple of items that can commonly cause this concern.
The first thing that you need to check is to see if the theft light is flashing when the Explorer wont start.If it is,then the PATs (passive anti theft) system an intermittent fault.The key may be faulty or there may be a wiring problem to the ignition key transponder.This is the unit that reads the chip in the key.Often when you have a tilt steering,the wiring to the transponder can develope a break and create an intermittent no start.
The next step would be to check to see if the check engine light comes on when you first turn the key on.If it doesn't,the PCM (engine computer) power relay may be faulty.
If these checks don't lead to a repair,you will need to check fuel pressure with a gauge during the no start.There may be an intermittent fault in the fuel pump.
Unfortunately with intermittent problems,it may take some trial and error to pinpoint the fault.I've given you some solid things to help narrow down the possibilities.
There are two anti theft systems in your vehicle.A PATS (passive) and an active system.The PATs inhibits starting only when the key isn't recognized.Look for the flashing theft lamp to see if this could be the problem.