I'm going to be as descriptive as possible with respect to this issue, so I ask that you PLEASE read this write-up thoroughly to limit redundant ideas/suggestions; so thanks in advance for your time...

What we're dealing with:
'93 DX Sedan w/ B16A2 running a chipped P28 w/ B16 basemap

The issue:
When it runs, it runs GREAT (no CEL or anything) -- but randomly while driving, the car shuts down... NOT just the motor, the whole sha-bang. All dash lights go out.

Upon sitting for a bit (5-10 minutes randomly), she will start right back up like nothing happened.

What's been checked/What we know:
- Cannot be the distributor, as it's not just the engine that stops running, the entire car looses power.
- I wouldn't think it's the main relay, as the lights on the dash would stay lit even if the fuel pump/ECU went out.
- Ignition switch was replaced with a NEW unit. (We were failry certain that this was going to be the problem, because the problem mimics turning the ignition off while driving)

Any other ideas?

 

Just a guess: Possibly the alternator itself is failing or loose wiring (poor contact) to alternator. Bring to Autozone or other parts store and have alternator amps and voltage output checked . Also, check (for loose) and clean all grounds to frame and block.

 

new as oem honda or parts store replacement switch?

 

Possible, but wouldn't the battery keep the car running during the time that the alternator was out?

"Quality" OEM-style replacement... But what would be the odds of getting a new switch that had a problem much the same?

 

More details are needed.

Is it a no crank problem or cranks but won't start problem?

When the car shuts off and won't yet restart, exactly which electrical components work and which don't? For example, do the hazard lights or horn work? Do the headlights work?

 

From your description: "When it runs, it runs GREAT (no CEL or anything) -- but randomly while driving, the car shuts down... NOT just the motor, the whole sha-bang. All dash lights go out."

This is obviously an electrical issue: alternator or wiring harness or loose contact(s) . If the alternator fails the battery may provide a very brief backup ..but, it wouldn't take long under load conditions for it to drain down to zero as it doesn't provide enough volts under load or the constant output needed.. One (old school) way to test an alternator is to start the engine and remove the positive side battery cable..if, the engine keeps running the alternator is good,, if the engine cuts out right away then the alternator or it's diodes is shot. Read: Car Battery or Alternator: How to Tell Where the Problem Lies - CarsDirect I recommend that you have the alternator tested at Autozone or other parts store first (rather than removing positive cable) as their scanner will show the alternators amps and voltage output. Lifting the positive cable while engine running is not recommended for modern cars. Read: http://www.2carpros.com/questions/19...lle-alternator

"Most alternators have an output between 13 and 14.5 volts that they try to maintain at a constant level. As more power is demanded by the headlights, the windshield wipers, your radio, the heated seats, the rear window defroster and so on, the alternator needs to work harder to maintain the necessary voltage. If your car's alternator is not working to its full potential, or demands are placed on it that it can no longer meet, the voltage will either go above or below the set level."
The battery's function is for starting purposes only (or for keeping the sexy music going while you work your magic on your woman) and once the engine is started the alternator handles necessary power needs from there. Since, the alternator is cool and likes to share..it charges the battery too. Read: Top 5 Signs of Alternator Problems - HowStuffWorks

Your car's issue is not unlike any other car issue... start with the simple, most common, and least expensive things first and work your way from there. Get your alternator tested for amps and voltage output and if checks out okay then move on to wiring harness: possibly frayed wires near intake or loose contacts,

 

A friend of mine just was experiencing this same thing, in a 99 civic. I have a 99 accord that was doing the same but mine was a bad ignition, which you seem to have already replaced so can't be that. Could it be the computer? My friends civic has sat at the shop for three weeks and they finally found the issue, his computer was getting too hot and has melted causing it to shut off randomly while driving.
Hope that helps!