This was similar to my issue on my '82 back in 2010. Read my post from back then and see if this will help...troubleshooting means covering all the bases...good luck!
I had a little bit of this problem with starting, and to stay running, while my '82 was in the shop for general maintenance. While moving the car outside, my mechanic said the car stalled and shut down. Eventually, with numerous troubleshooting attempts and replacing both air throttle valves to no avail the car would not stay running.
Searching the car from front to back, we eventually found that the fault was in the fuel tank. Not the sending unit mind you, but the attaching hardware had failed. The sending unit has a hose held by 2 teflon clamps that is in turn attached to the fuel line leaving the tank and going to the engine/fuel pump. While both of the clamps over time had become 'brittle', one of them actually broke at the geared teeth and allowed the hose attached to come undone and pretty much just rerouted the fuel right back into the fuel tank...allowing just enough fuel to reach the injectors and start the car for a few seconds.
So, I would also look at the sending unit assy and make sure all of the hardware that is attached, is in fact, attached and in good condition.
I replaced those teflon clamps with typical radiator hose clamps. The car runs like a champ now!
And keep in mind, this issue is only for the '82 MY...the only C3 with a in-tank fuel pump.