'98 Honda Civic with "undiagnosable" ailment

My car is a '98 Civic LX that I bought from the original owner 11 years ago. So I’ve had it for the better part of its lifetime and have taken great pains to maintain it well and keep good records of all work done. That said, I don’t have a clue about cars.
In early 2012, the check engine light came on, with a 0420 code. I had it checked by my regular mechanic, and they told me not to worry too much and cleared the code. It stayed off for a few months before coming back on with the same code. They told me not to worry about it until it started running rough, which it did in April. They replaced the rotor button, spark plug wires and distributor cap at that time. About a week later, the car made a rapid clicking noise and cut off while I was driving. It started right back up and the incident was not repeated. In May, the light came back on. At that point, they replaced the full catalytic converter and sensors, etc. Since then, the car has cut off a few more times. I’ve had other repairs done (leaky oil pan gasket replaced, transmission fluid service, CV axle), and they have never been able to replicate the stalling in the shop so they’ve told me not to worry about it. On April 5, 2013, the light came back on. I took it in and it gave the same 0420 code. They “couldn’t find anything” and cleared the code. The light came back on the next day. I took it to another garage on April 11, just to get a second opinion. They “couldn’t find anything” either but did tell me the catalytic converter, etc. was all new. They cleared the code. It came back on about a week and a half later. I wasn’t driving it much and did not have time to get back to the mechanic. On April 30 it stalled again while driving. On May 1 it cut off twice in one drive and I had to crank it several times to get it running again. I took it back to my regular mechanic and they kept it for several hours before telling me that it was cutting off when they jiggled the ignition wires. They replaced the ignition switch. (Are you beginning to imagine how much $$$$ has gone into this car in the last year?)
The car cut off while driving again on May 2. The light came back on again yesterday, May 6. I took it back in and they “can’t find anything wrong.”
I’m only hanging onto this car because I have a 16-year-old and this is the perfect starter car – if it will keep running.

I’d really appreciate any ideas!

I normally suggest testing instead of throwing parts at a problem.
But with an intermittent problem that’s hard to catch in the act sometimes you have to start changing parts (less expensive first) and cross your fingers.

I think there’s two separate issues.
First, the many cat converters are needlessly changed due to the P0420 code.
It means the converter seems to be not doing it’s job correctly.
A good converter can’t work right if the exhaust gasses going into it are “wrong”: garbage in, garbage out.
I would check out the spark plugs, coil, fuel pressure.

On Hondas with stalling the ignition switch would be my second suspect.
The first would be the main relay (aka fuel pump relay).
It’s not very expensive and it’s old enough to just change on g.p.

Hi Circuitsmith,

Thanks for your response. Since the converter has been replaced and the spark plug wires were done, too, should I ask them to look at the coil and fuel pressure? Or is there some other aspect of the spark plugs? (I apologize for my extensive ignorance!)
I will also mention the fuel pump relay.

Anyone else wanna second this?

Your car is under a Recall for the ignition switch so that could have been done free of charge at any Honda dealer and you likely have 2 separate issues.

Based on the clicking noises, that could point to an intermittent main relay but the relay is influenced by a number of other things. The relays are a known problem though.

Regarding the 420 code, comments about replacing plug wires and so on along with the jiggling of wires I might ask if they replaced the spark plugs. Problems with wires and so on are usually caused by aged, high miles spark plugs.

I’ll second looking at fuel pressure. If it’s cutting off while you’re driving, that could indicate a tank venting problem. Try removing the gas cap and driving around for awhile (this may cause it to throw another code, which you can safely ignore for the duration of the test). If it stops dying in traffic when you remove the gas cap, your tank is not venting properly.

I’m so glad to get so much feedback!
As for the recalled ignition, it was replaced years ago.
I’ll focus on the relay/spark plug/fuel pressure when I speak to them today. They’ve had it for a day and have not diagnosed anything yet.
Anything else it might be?