Lumina Hesitates

Hi everyone. I have a 95 lumina. Only 50,000 miles on it. When low on gas, soon as you start it shakes viloently then dies. Will restart after 15 minutes, drives fine. Only happens everyonce in awhile. I have had towed, they can't find problem.
Now, when I am driving, when I accelerate, it hesitates, jerks...so, I let it coast adding just enough gas. But, it did NOT die. Drove agon in a coupkle hors, no prolblem! I have had it looked at several times them saying no problems! I am afraid to drive this tempremental beast! Any ideas?

Thanks in advance! Jen

Welcome to AF, how recent is the fuel filter and get a fuel pressure gage on it and monitor the fp during the event, look for 37-40 psi.