The most failure-prone component in the cold-start injector system is the time/temperature controller that shuts off the injector after a certain amount of time, or after the engine hits a certain temperature. There may be different configurations in different years, but there has to be some sort of time/temperature controller, probably on the side of the engine.

Mine failed on my 1991 when the car was a week old, and has not failed again since. My sister's failed on her Toyota Celica at about 100k miles. In both cases, however, the failure mode was to fail to shut the injector off, rather than to fail to open it.

When my '91 brick was two years old, it flooded while on a trip to Iowa in winter. I figured the cold-start injector time/temperature controller had failed again, so I unplugged the cold-start injector until I got back to my garage in California. While in Iowa, the car started immediately in temperatures down to around 10F, without the help of a cold start injector. When I got back, I plugged in the injector again to test it, and it worked just fine. I never figured out why it had flooded.