86 Ski Nautique electrical/ignition issue

The coil, module and resistor need to be matched and wired properly (per the provided instructions). Sounds like there is some sort of mismatch going on. Without knowing the brand/model of the EI kit, we don’t have enough info to answer the question. Do you still have the install instructions that came with the kit?

What is the voltage (feeding the coil) when it starts to run rough?

Here is a post from a few years ago discussing the different ignition modules and the requirements for each. Look at Hollywood's post about halfway down the page.

old post

Here is the text:
Eh, I'm not going to take his word on all EI modules. These manufacturers seem to be pretty specific about what resistance they want.

SkiDIM currently sells the Pertronix Ignitor II, which in their product description does state to bypass the resistor. Pertronix Ignitor II instructions agree.
6. The Ignitor II ignition can be used in conjunction with most ignition coils rated at
0.45 ohms or greater.
7. All external resistors must be removed to achieve optimum performance from the
Ignitor II ignition system.
http://www.pertronix.com/docs/instruction-sheets/91141.pdf

HOWEVER, some of you may have had the Ignitor I, which DOES state a minimum resistance.
Pertronix Iginitor (the first edition) installation instructions:
4. Four and six cylinder engines require a minimum of 3.0 ohms of primary resistance and eight cylinder engines require a minimum of 1.5 ohms of primary resistance. Do not remove resistors if the coil primary resistance is less than specified.
5. If your Ignition coil has the recommended primary resistance, remove or bypass all external resistors.
http://www.pertronix.com/docs/instruction-sheets/1141.pdf

Hot-Spark:
Coil Warning: DO NOT use a low-resistance or an HEI-style coil. 4- and 6-cylinder: Use a coil that has resistance in the primary circuit of at least 3.0 Ohms (Ω). 8-Cylinder: Must be used with a coil that has resistance in the primary circuit of at least 1.5 Ω. Using a coil with insufficient primary resistance can cause the ignition module to overheat and misfire until it cools down again, or fail prematurely, which will void the Hot-Spark ignition warranty.
http://www.hot-spark.com/Coil.htm

Mallory:
NOTE: The purpose of resistance wire between the ignition switch (12V) and the ignition coil positive terminal is to restrict current flow through the ignition coil. Failure to use resistance wire will eventually destroy the Ignition Module.
http://prestoliteperformance.com/media/instructions/mallory/Mallory_Instructions_unilite_distributor_37_38_45_47.pdf

All that said, know what kit you have and what they want. Seems as though Pertronix Ignitor II is the only one that is safe to bypass the resistor no matter what coil you are using. And now I think most of you burnt up your EI modules on your own. SNobsessed, if I were you I'd wire back in the resistor.

Yes!!   I replaced the distributor and that cured the problem.  you can get a new Mallory distributor from Nautiqueparets.com or skidim.com.  The other option is a DUI.  Let me know how you come out.

I have not heard a peep from my customer.  No calls from him is good news to me!  The distributor was the last thing I replaced.  No more issues.

My test was the engine would get to where it would not run and everything else had been checked or replaced so I replaced the distributor and now it runs fine.  I just replaced a complete distributor on a GT40 and now it runs fine as well.