Weird CCRM problem

[Estlander]

I have a 1993 Taurus 3.0 Vulcan.
I've been having starting problems and sometimes ,while driving, the engine stalls for a couple of seconds and sometimes dies on me completely.
I learned that it was because of fuel pump not coming on(no humming sound coming from the tank).
I thought it was my CCRM box, so i bought a new one, but the problem remained.
So, i know it's not my CCRM box. But the weird thing is that every time the engine dies on me during driving, i pull over and open up my hood and knock or bend the CCRM box up and down, after that i hear that click inside the CCRM and the fuel pump powers up and i can continue driving.
It sound almost as if one of the wires that go inside CCRM is broken or something. But how can that be? I mean, the CCRM box is under that plastic panel, therefore it's not a place where wires could break because of too much movement.
Overall it doesn't sound like it's anything serious, but sometimes the simplest problems can bring so much headache.
So i ask you guys here to offer me your ideas as to what could be wrong or what to check.
And the other thing is that because of the problem that i'm having - an engine dying during driving and the car still keeps on moving without the engine working until i can find an appropriate place to stop, then could it hurt the automatic transmission?
Or in general when a car with an automatic transmission runs out of fuel, or in my case the engine dies because of fuel pump turning off?
Thank you!!!