1991 Dodge Dynasty stalls about ten miles into trip

Car starts and runs great for about 10 miles then just shuts off as you are going down the road. There is no warning of problem of any kind but just
stalls. It will usually restart about 10 to 20 minutes latter. I have tried several ideas including new rotor and distributor, new computer module, and new key ignition switch. I have also checked to see if I have gas pressure at the valve in the line and it appears it still has pressure when it dies. Any suggestions would be appreciated?
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1. What happens if you start it up and just let it idle for the same amount of time the 10 mile trip would take? (might point to it being heat related as opposed to motion related) 2. If the same thing happens with just idling for that amount of time, does it also happen if you let it idle with the hood open? (i.e., no heat buildup around any components) 3. Does it happen if you leave the gas cap open? (might point to a venting problem, causing a vacuum in the fuel system as you try to draw gas)
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please involve engine size also.
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