Fuel delivery or Electrical?

[Orocular]

Hello. I have a 98 Mustang hardtop. My sister in law owns a 98 convertible. She has the V-6 3.8L(?) I think. But it’s the factory 6 anyways. It has about 85k miles on it and seems to run fairly decent. She has been plagued with an issue on hers though, and we can not figure it out.

On occasion when she kills the engine (EI shuts it off to go into the store) it will not start back up. It has been happening more and more frequently and we have taken several steps in order to try to remedy the problem. We have replaced the fuel pump, and the fuel pump assembly. We have tried to do the fuel filter, and still the same problem persists. The car will start a little bit later on its own, when it decides to... usually the next day. My question is what the heck can it be? We are thinking possibly a electrical connection or maybe something in the gas tank (IE marbles or such?).

My sister is thinking about getting rid of the car due to this issue, however she has it fairly customized and has been working her rear end off to make the payments, and still owes a good amount of money on it (no positive equity) so we are pretty much stuck with the car. I hate to see her get rid of this car as she really has been busting her rear to not only keep it, but have a little extra to spend on herself. I hate to see the neon and other customizing she has done to it go to someone else... not to mention it has the Mach 460 stereo in it.

Anyone got any thoughts?