If you are certain that the baffle is solidly fixed in place, the next thing is to look at the electrical side of things. The computer monitors the pump power and will set code 95 or 96 if the relay drops power to the pump. Therefore, dump the codes and see if you have code 95 or 96. These two codes do not set the CEL, so they could be present and you would not have any warning.
The problem with the loss of pump power is that codes 95 and 96 only detect loss of pump power at the pump side of the fuel pump relay. It does not actually see if the power wire directly on the pump is getting power.
if you have not already done so, plan on dropping the fuel tank inspect the external wiring pump wiring and ground. Also plan on removing the fuel pump to check the internal wiring and the baffle. Judging from the symptom description, I would place a loose baffle at the top of the suspect list, followed by the inertia switch.
The code 95 and 96 use the same test test path. Code 95 looks for ground problems, while code 96 looks for loss of power problems.
Code 95 causes & tests 91-93 models. –The 95 code is because at one time or another, the fuel pump relay hiccuped and didn't provide power the pump when the computer told it to run. Sometimes this is a one time thing, other times it is a no run or runs poorly condition.
Suspect items are bad fuel pump relay, corrosion in the fuel pump relay socket, inertia switch, wiring damage , corroded connector contacts.
Look for a failing fuel pump relay, bad connections or broken wiring. The fuel pump relay is located under the Mass Air Meter on Fox bodied stangs built after 91. On earlier model cars is under the passenger seat. On Mass Air Conversions, the signal lead that tells the computer that the fuel pump has power may not have been wired correctly. See
Mustang Mass Air Conversion | StangNet
Diagram of the fuel pump wiring for 91-93 cars.
Look for power at the fuel pump - the fuel pump has a connector at the rear of the car with a pink/black wire and a black wire that goes to the fuel pump. The pink/black wire should be hot when the test connector is jumpered to the test position. To trick the fuel pump into running, find the ECC test connector and jump the connector in the lower RH corner to ground. No voltage when jumpered, check the fuel pump relay and fuse links.
Power feed: Look for 12 volts at the pink/black wire (power source for fuel pump relay). No voltage or low voltage, bad fuse link, bad wiring, or connections. Remember that on 92 or later models the fuel pump relay is located under the Mass Air meter. Watch out for the WOT A/C control relay on these cars, as it is located in the same place and can easily be mistaken for the fuel pump relay.
Relay: Turn on the key and jumper the ECC test connector as previously described. Look for 12 volts at the dark green\yellow wire (relay controlled power for the fuel pump). No voltage there means that the relay has failed, or there is a broken wire in the relay control circuit.
91-93 Models:
Using the diagram, check the dark green/yellow wire from the fuel pump relay: you should see 12 volts or so. If not the relay has failed or is intermittent. Check the inertia switch: on a hatch it is on the drivers side by the taillight. Look for a black rubber plug that pops out: if you don't find it, then loosen up the plastic trim. Check for voltage on both sides of the switch. If there is voltage on both sides, then check the Pink/black wire on the fuel pump relay: it is the power feed to the fuel pump. Good voltage there, then the fuel pump is the likely culprit since it is getting power. No voltage there, check the Pink/black wire, it is the power feed to the fuel pump relay & has a fuse link in it. Good voltage there & at the dark green/yellow wire, swap the relay.