Engine shuts off while driving?!?

i have a 1993 ford mustang 4 cylinder engine. oddest thing has been happening for about six months. while on an incline (or more specifically, when i am not using the accelerator), the battery light turns on and the engine shuts off, leaving me coasting toward a shoulder. i still have lights, radio, heat, etc. when i try to start it up again, it starts up right away. it tends to happen in the morning (after being parked overnight). but it only happens about once a month. i had two mechanics look it over and they were both baffled (plus it’s hard to check out an intermittent problem). battery is good, fuel injector is clean. people are telling me to get a new car saying my car is tired. well, i don’t know much about cars, but i do know that it is not mysteriously tired; it’s a car with a real problem that has not been pinpointed yet. HELP!

There’s a lot of things that it could be but tired is not one of them.
It’s near impossible to make much of a guess without knowing if the problem is fuel or spark related. Knowing that could help to narrow it down a bit.

Since it starts right up again this makes it much tougher.

To aid in my wild guessing here, when it quits does it shut off instantly or does it buck or hiccup for a second before it does quit?

Drive the car up on car ramps, and let the engine idle. Drive it down, and back up. Does it cut off? If the problem is reproducible, a cause is more easily found.
RSVP with results.

About the only thing that makes an uphill engine quit is the fuel pump.

I think it is downhill, since the OP mentioned not using the accelerator.

Try this. With engine at idle, press and hold the brakes as hard as you can. If the engine stumbles or stalls, look to a brake booster leak.

Also, it could be a dirty IAC port. Maybe cleaning the throttle body may clear it up. When rolling downhill, foot off the accelerator, the IAC closes until your near stopped, and it re-opens to maintain idle. Crud and sludge can delay this action just enough to stall it out.