I am not sure wether the Duke is injected or carbed. If it is carbed and heaven forbid the engine stalls at idle, and you don't flip the switch fast enough you might possibly have to change your name to Fastburn. 
Harry
The duke is injected. It has a throttle body injector that sits above the butterfly and spits fuel directly into it.
Quick answer...no, jumping the pin in the ALDL will not hurt anything. By doing this, you are simply bypassing the the relay for the fuel pump. But Fierofool is right...if this is resolving your issue, you are simply bypassing whatever is amiss. Intermittent problems are the hardest to diagnose because all testing must be done while the problem is happening (in this case, while the engine won't run...so, before and after each test, see if it will start...if it does, the test is null and void). I am making a couple assumptions here based on what you have said...if any of these are wrong, then the rest of what I say may not be accurate.
1. Fierofool's test failed...fuel pump still wouldn't kick on after waiting a moment and then turning the key back on.
2. The car is dying consistently after around 30 minutes (but not the exact same amount of time each round).
3. Jumping the ALDL resolves the issue every time (and has been done several times...my motto is "Once is coincidence, twice is luck, three times sets the rule").
4. We know the fuel pump is not running while we are having this issue, unless we jump the ALDL (which resolves the issue).
So...we know we are dealing with fuel pump wiring. This tells me we are dealing with one of two issues.
1. A broken wire (the orange one) prior to the fuel pump relay. You said you checked the fuse, obviously that is the first step. I would replace it anyway, but that is unlikely to be the issue. Second step would be to check for voltage at the orange wire at the fuel pump relay WHILE IT WON'T RUN.
2. If there is voltage there, then we are actually dealing with two issues. There is a secondary path for fuel pump power that bypasses the relay. It runs through the oil pressure switch...as long as you have oil pressure, there should be power to the fuel pump through the secondary circuit. You can check the oil pressure switch quickly by disconnecting the relay while the engine is running (normally, not with a jumpered ALDL)...if it dies, then you have a bad oil pressure switch. Lets check that out first. If the oil pressure switch is bad...although replacing it would resolve the issue of it dying on you, we are still bypassing the real issue, which would be in the area of the relay. Remember that all tests must be performed while it won't run. We already checked for power getting to the relay in step one (and you already checked the relay), so now we will check the other wires.
1. With the key in the run position, check for voltage at the Dk Green/White wire at the relay. This must be over 10 volts to flip the switch in the relay. This will confirm whether or not the ECM is telling the fuel pump to run.
2. Check for continuity from the tan/white wire at the relay to the fuel pump. This will determine if power can get from the relay to the fuel pump. To make this easier, this test can also be done between the relay and the pin on the ALDL since we know power gets from the ALDL to the fuel pump when you jump it.
3. Check for continuity between the black wire at the relay and a solid ground in the car. Obviously, this will confirm the ground side of the switch.
I can't stress this enough...we must make sure you are still having the issue before and after each test...if you test one of the wires, and then it starts, then we need to wait till you are having the problem again and retest it.
