Stalling while driving

Thank you very much for the reply. Certainly I will check all that. The problem is (like I mentioned above) that when the car shuts off it doesn't start up again. There is no hum from the pump when I try to prime the pump (key on-engine off). But it will start immediately if I disconnect one of the quick connects at the fuel filter and connect up again. At that time I can hear the pump hum and it starts right up and runs for hours. It happened 3 times already. It shuts off, unclip the connect at the filter and starts up every time. Also, I forgot to mention before that I have a fuel leak from the top of the tank (possibly bad seal) when I fill up the tank completely. Gross evap leak code.

The vehicle ran for a year with the gross leak code on without a problem.
Everything you mentioned is good advise but it does not explain why the vehicle starts only if I disconnect and connect back on one of the quick connect clips in the fuel filter.
It seams to me that you don't read properly what am I saying. Please reply.
Thank you.

No pressure escapes, no vacuum as far as I can tell. And some fuel is coming out of the filter. Than I connect the coupler and turn the key on, I can hear the pumps hum, crank the car and it starts right up and runs for hours. It happened 3 times already. Then I shut the car off and I restart in 1 or 3 or 6 hours and starts right up and stays running for as long as I keep it running. It makes no difference how cold or hot is outside, it will start every time. Now you have to realize that I run the car in the driveway, I don't take it on the road because the 3 times it shut off it was when I was driving. I have no hesitation whatsoever when it runs in the driveway or when I was driving it. Perfect idle. No back firing, just shutting off of the blue.
And every time it shuts off it wont start again (just crank) in 1 hour or next morning or 3 days later. It starts only when I do the voodoo thing with the filter. Also it will start when I use starting fluid and will run for 30-40 seconds. It does not make sense. And I know that you are doing your best to figure it out and help me and I really appreciate that.

That makes a lot of sense. The only question I have how I will connect the pressure gauge in the fuel pressure line? Do I need a special adapter? Because the pressure gauge has at its end the fitting that connects to the shrader valve at the fuel rail.

After numerous attempts to find an adapter for the gauge, I decided to drop the tank and I found that the metal jacket that covers the clip for the high pressure line was completely rusted and the clip was stuck almost half way in. Than using a pair of vise grips I was holding the clip to the pump inlay as in as possible. A friend of mine connected the gauge to the shrader valve and I turn the key on. Pressure jumped to 36-38 psi, I released the grip, pressure down to zero. So now according to your thinking I replaced the weak pump and after an extensive search I found only on e-bay a fuel line set that was a fit for the 1999 Jeep. Started right up, pressure instantly at 60+ psi.
I'm extremely grateful for your expertise and your instructions, because you were the only ones that tackled the problem. Before I contacted you I did a search for answers on google and I ask a lot of so called "mechanics". Every answers I got were: crank sensor, cam sensor, for sure ECM, bad battery, alternator, plugs, wiring, relays, fuses etc, etc, and I knew that all of that was a bunch of nonsense. Then I remember that years ago I used to watch your TV program that I really enjoyed and I Googled searched you. The rest is history.
Thank you very very much again and I wish you happy holidays. I will keep in touch.