1986 Honda Accord Random dying

My wife drives a 1986 Honda Accord. Recently she was driving and it just died. No sputtering, just quit. It would not start again for another 5 or 10 minutes, would act like it was going to turn over but then die. After 10 minutes, it started again and ran well, but then after not driving more than a mile or two, on her way home the same thing happened, and the same results. It is not running fine again. The mechanic checked the alternator, and a few other things, but didn't see anything too bad. There is a leak in a part of the carburetter, but the car just idled low, the mechanic changed the idle and it now idles well. Any suggestions. I would love to try to fix this myself, but need to find out what is wrong. Since it won't stay dead it is tough to trouble shoot and I do not want to have a mechanic out again just to pay him to tell me nothing.