I have a 91 CRX Si that until now it’s been the perfect car! I’ll describe the problems. I don’t know if they are related, but I’m starting to think maybe they are (in some strange way). About a year and a half ago I went to start it up. It fired right up like usual but then just stopped and refused to restart. It was a dry cool (65 F) morning. It sat the whole day and when I got home from work the beast start right up. It drove fine (re: “fine” see note below) for about 8 months. And then did the same thing. I checked the main relay, spark, fuel etc. Replaced the plugs, cap rotor, and fuel filter just to be sure. But no start! After 3 days I got fed up and had it towed to the dealer. It started right up for the dealer and they could find nothing wrong. As before it’s been driving fine (re: “fine” see note below) until now. Now I have an intermittent problem. It suffers a stumble or hesitates when accelerating. It seems like it’s missing on all cylinders sometimes. Other times it’s just a short miss, like one cylinder. I can’t tell if its fuel or electrical related. Like I said, it’s intermittent. It doesn’t last very long but the sudden loss of power in the middle of a busy intersection is a bit scary! I did find a large crack in the center post of the cap. I replaced the cap, rotor, plugs, wires and fuel filter (again, just to be sure), but no change. I can drive for 40 miles before it happens or just a few feet! When sitting in the driveway everything checks out normal and I've checked every electric connection I can get to. No check engine light and the ECU blinks no codes (it does blink once when started, as it should). I’m thinking bad coil or igniter. Do these items suffer “intermittent” problems before completely dying?
Note: this maybe related. A long time ago it developed a little problem when it “heat soaked” a bit. When restarted (hot) the revs would drop when idling but then pop right back to normal. This went away after driving a few miles. I replaced the EACV and this did seem to solve the problem.
Anyone have an idea? Driving my 14 mpg Jeep is getting a bit expensive!
Sorry for being a bit long winded!
Thanks
Jeff

Can you specify how EXACTLY you "checked" your main relay? Did you resolder all the joints, or just took a look at it?

To be honest with you - I'm experiencing the same problem (loss of power and some hesitation) between 2000 and 3500 rpms sometimes when I step on it while it's still at 2000. My engine is also burning A LOT of oil. I was unable to pinpoint the problem. My fuel filter, spark plugs, spark plug wires, distributor cap and rotor, air filter are all new and ECU reports no codes. I've ran fuel system cleaners a few tanks, and still no help. I will check timing as soon as I find a Timing Gun (or whatever it's called). Only thing I noticed is that probably my exhaust pipes have a hole somewhere between the cat and the muffler (the car sounds different than it did when I got new exhaust piping), but I don't know if it might be causing the problem.

Do check coil and igniter (a procedure you should follow is written here - https://www.askmehelpdesk.com/showthread.php?t=9924).

Cro, did I ever suggest a sludge removing treatment such as Auto Rx? Oil usage may be due to a stuck ring. The over an oil change interval cleaners tend to be more effective and less damaging to the engine than the engine flushes.

You did recommend it, and I did search for it here in Croatia, but there seems to be no shop that's selling it. My car is burning about a liter of oil on 500 miles (no, I didn't mean 5000 miles, but 500 miles), and I'm planning on putting a 130HP engine in it in a short time, so I'll just stick with this engine for a short while, and then attempt to rering it myself, once it's swapped out. Anyway, I do not change oil any more, it's burning it that much that it's constantly running on new, fresh oil I'm adding to it.

----- EDIT -----
I forgot to mention that compression readings are within manual specifications. Top compression should be 12.7bar, minimum should be around 9.5, and all my cylinders show 11 or more.

----- EDIT.2 -----
Engine head has recently been rebuilt, with new valve seals, so no oil should be burning through them. Also, valve guides have been inspected, and did not need replacing.

I checked the relay per shop manual procedures. Very time consuming! In fact I just started at the beginning of the manuals troubleshooting procedures and checked everything possible. I don't have a ECU test harness so I did the best I could to "measure around" things.

The only odd thing I did find was the resistance of the primary coil side. It was 1.1 ohm. A little bit above the specs of .60 to .78 (if I remember correctly). But I can't see how this could really have any effect.

Well, it's 50% over the max resistance... see if someone has an extra coil that's good (maybe a friend or someone... join a local Honda Fan Club? :) ) and try it out for a few days - see if it's any good.