I've been working on trying to get a Bertone X1/9 running and I have come across a problem. Here's a synopsis of what I know:
The fuel system is working: good fuelpressure and flow, and there appears to be appropriate fuel being returned to the tank from the pressure regulator.
The ignition appears to be fine too, since the car starts up easily and runs smoothly for a few seconds, but then fades out. If the ignition was an issue, the engine would either not run, run roughly or just quit abruptly, which it
does not.
The fuel injection also appears to be working okay as
indicated by the smooth engine operation, at least while the engine is
running.
It appears to be an engine computer issue. Apparently, the computer
begins sensing various engine parameters a few seconds after the engine
is started. Then, I am guessing that it must be leaning out the
fuel/air mixture to the point where the engine can no longer keep
running.
I notice that if I pump the foot feed right after starting the
engine, it will run a bit longer than if I don't do this, but it still
quits after just a few more seconds.
One guy I heard from thought it may be the air intake sensor, which is
basically a vane in the intake manifold that moves when air is sucked
into the engine. The engine computer then regulates the mixture based
on where this vane is, and if the vane and/or sensor is not working
properly, incorrect information is sent to the computer which results in
an incorrect fuel/air mixture.
I have not had a chance to check this out, nor do I really know how to test this sensor to tell if it's working properly.
If anyone knows anything or has any ideas I sure would appreciate it. I really want to get this thing running. It looks like a real fun car.

I'm no expert but I agree that the air intake sensor is a good place to check. To see if that's the case disconnect the duct to the throttle body and get some starting fluid (spray) then spray in short bursts before the engine cuts out to see if it stays running. If the fluid keeps its running for a few more seconds then good chance it's the sensor. I have done this to other fuel injected engines. I hope this helps.

I'm no expert on the fuel injected X1/9s but what you've described sounds like a closed loop problem - typically the result of a faulty lambda sensor. It takes time for these sensors to react to changes in gas composition and most importantly to gas temperature.

Problem is that I don't know if the X1/9 has a closed loop system for idle - I know later generations of the engine do but not the earlier ones.

The other important part of that circuit is the MAF sensor (air flow) which has already been pointed out.

how would i go about testing either of these sensors?

okay i tested the air flow sensor and it works and if the oxygen sensor were bad i would think it would still start and run just not very good. It starts up first try every time and runs and sounds good but it dies right away. Its so confusing. what could it be?

Have you checked for air leaks in the induction system (between the MAF sensor and the head). Check injector seals, gaskets, pipework, etc. Any leaks will make the readings from the MAF sensor fairly worthless.

okay i can and also i do have the fuel pump wired to run all the time right now. could that be something?

Having the pump running all the time shouldn't be a problem at all - it just means that the fuel rail is up to pressure immediately.

Okay well ive been doing some work today to get the relay working right. Ill probobly have it working the OEM way by the end of the day. I just wondered if for some reason having the fuel pump run all the time would cause too much pressure and the ecu would tell the injectors to shut off. But i don't think thats my problem. So if it is getting fuel and spark what else could it be. And i checked the MAF sensor and it seems to work just fine.

Have you checked the spray pattern from the injectors?

I know it is a bit messy and potentially dangerous to spray petrol all over the place but you may want to remove the fuel rail (with injectors) from the car and test run it (spraying into a suitable container and with the ignition on the car disconnected as a precaution) to make sure the fuel is coming out as expected. It will kill the battery fairly quickly and it isn't brilliant on the starter motor but you will be able to visually check that it works.

It could be one or more of the injectors is dying and stops spraying once it gets warm (and they do get warm). The fuel passing through them is supposed to keep the temperature down but it isn't that effective...

alright i can check them. also i got diagrams to the whole electrical system so i am going to check that too

okay ive been working on pulling the injectors and its crazy how you have to pull the whole intake manifold off just to get them out. its alot different than the honda engines im used to.

Okay only 2 of the 4 injectors work and I can figure out how to A) get them off the fuel rail or B) take them apart. If anyone knows how to fix them or where in the world i could buy a whole new set/ fuel rail i would really appreciate it.

If they are dead you can try "shocking" them back into life using a 24v battery (from a truck or from a pair of 12v batteries in series). Obviously you need to completely disconnect them from the rest of the car electrics as other components are not so tolerant.

The nicer but more expensive option is a sonic clean - you should find plenty of injection specialists capable of doing that job.

If you go for a replacement you need to find the part number on the injectors you have and get in touch with a regular supplier. They weren't very widely used but should still be available.

A complete fuel rail is likely to suffer the same problem - the injectors become stuck pretty quickly once removed from the car (I'm guessing the lack of oil and fuel to dry the air is the fault as they seem to stay working if left in a car). Try getting in touch with the guys on xweb as they have plenty of reliable state-side suppliers - your problem is far from unique, I think most of the FI guys have suffered along these lines)