My 1988 Honda Prelude not starting

I have a 1988 honda prelude 2.0 si feul injected with 176,359 miles on it automatic. I recently have had trouble starting the car. I would try to start it and it would take several tries till finally it would not start at all. I took it to a mechanic and he said my valve cover leaked and the oil burned out my distributor. He replaced the distributor, valve cover gasket, plugs, wires, cap, rotor. When I got the car back it ran for about three days before doing the same thing. He then replaced the distributor for a second time claiming it was faulty. Got the car back and again ran perfectly fine for another 3 days before doing the same thing. He replaced the distributor for a third time plus my battery and once again the same pattern. I don't wan to shell out any more $ unless it's worth fixing. It just cranks but won't turn over. Eventually I smell gas after trying over and over which should rule out the fuel pump. Any suggestions would help. Could it be the ignition coil and how can I test the distributor to make sure it works? Thanks in advance.