mr2 intermittent shut off

Have a 1987 Toyota MR2.The problem is sometimes it will start right up,other times it will crank over but does not fire.Started checking connections and cleaning and putting on dialectric grease and each time I did one I would try to start the car,it started.But right back to the same issue.When the car does start,it will run perfect for about 15 to 20 minutes and then its like somebody just shuts the car off.And it wont restart.Any help or suggestions would be of great help.Because if I cant get it straightened out,it's going to scrap.Cars in good shape but I am at my wits end.