If the injectors click then the hall sensor is working, at least when you tested it. You may have been asked this before: when the engine dies does the tachometer drop immediately to zero or does it fall slowly as the engine slows? If it drops suddenly then something on the low voltage side of the coil is failing. If it drops slowly then it is in the high tension side of the ignition or you have lost fuel. A pressure gauge Teed into the cold start injector line will tell you if you have fuel. An obstruction in the exhaust system could also cause these symptoms. When we were kids we would stuff a potato into a tail pipe as a practical joke. The car would stop running soon after it started.
76 Suzuki GT500
2011 Jaguar XKR
A little government and a little luck are necessary in life, but only a fool trusts either of them. - P.J. O'Rourke