Engine not running

Fuel pump could be failing-check/monitor the fuel pressure-start here

As stated above, check fuel pressure. You could be experiencing what's known as "vapor lock" where the fuel pressure is too low to overcome the heat of the engine compartment and the fuel vaporizes in the lines.

Yes, we're both very experienced Ford techs. But, I misread your original post. I missed the "it doesn't crank" part and presumed it cranked, but wouldn't fire.

Check starter draw. Both when it is cold, and when it gets hot. Also, when hot, verify that there is power to the starter, and that the solenoid is activating. Also check battery voltage and electrolyte level. And yes, you CAN do that on supposedly 'maintenance free' batteries.

Also, since I used to OWN a 2.4L Contour myself and never had this problem, I wouldn't consider it a 'known issue'. Just because one or two people have the issue, doesn't make it a common or known one.

Go to this link: https://www.2carpros.com/articles/car-cranks-but-wont-start

If its cranking over and w/n start -Do below

Get a helper disconnect a sparkplug wire or 2 and ground it to the engine atleast 3/16 away from ground-have helper crank engine over-do you have a snapping blue spark? If so-you have a fuel related problem, Do you hear the fuel pump come On when you turn key on? If not check fuel pump fuse and fuel pump relay if so, check the fuel pressure to rule out the fuel filter/fuel pump/pressure regulator and listen to the injector/s are they pulsing or hook up a noid light. No snapping blue spark continue to troubleshoot the ignition system-power input to the coil/coil packs,coil's resistances,cap and rotor,distributor pick-up coil, ignition control module, cam and crank sensors and computer Note: If it doesn't apply disregard it and keep testing

Check to see if the fuel pump is receiving power when the problem occurs. Kater, will it crank when the problems occurs, or does nothing happen when it occurs?

Absolutely, what's the verdict on power to and from the starter solenoid when the problem occurs?

No crank at all/nothing/nada when key is engage to starting position

Could be the starter relay, park and neutral switch/transmission position switch and ignition switch assuming the battery and connections are good. Note:If it doesn't apply disregard.

Do you have spark? And do you have the correct fuel pressure?

You got spark and fuel now its time to check the valve and ignition timing.

BTW do you have injection pulses?

Make sure you have the plug leads on in the correct order .. if they are not on correctly the car will not fire up ..

Double check the valve and ignition timing could be off 180 out start here