/// Which ignition do you have? There are problems with some alternate ignition systems. Poor contact with the ignition module is the most likely source of the problem.

There are other sources including battery cable defects. Look for obvious poor contacts in the ignition system then before you spend big money check the primary circuits, charging and wiring to fuses from the distribution rail. The negative battery cable can be tested by clamping a set of jumpers from the battery post champ to ground. (Use both sides on both ends. The positive system wire can be tested by running a jumper from the positive post clamp to the distribution rail. The positive cable to the starter should not be involved in the running of the engine.

The battery acts as a large filter for alternator output (noise). Some but not all cars will not or may not run on alternator output alone.