I had a 1990 Omni 2.2 that did that. It got progressively worse. It would act like you shut off the key. Sometimes you could turn the key on and off several times, and when you saw the tach needle jump it would fire. Whenever I did a diagnostic on it, it would say that the ac cutout relay was faulty. Which was odd because it never came with ac. Broke my heart to get rid of it because it ran great otherwise.