I would assume you are getting spark, since the engine eventually starts and runs. When she's running does it run well? If it does run well after you finally get her started, chances are it's a fuel related issue. Possibly the carburetor. As posted earlier, a manual is always a plus. Although when it comes to vintage anything with engine, you really need to know and understand at least the basics of how your system works, and then that sometimes is not enough. For example: I had an old John Deere tractor to would on occasion sputter and cough. I had good spark at the spark plugs. I had completely re built the carburetor. But this intermittent problem was driving me nuts. I eventually found a small amount of "crap" was in the fuel tank and would upon occasion temporarily plug the idle jet within my carburetor. The engine would keep running, although poorly for awhile, and then snap right out of it and run like a million dollars. My point is this, narrow it down as best you can. I would say the fuel system is a good start with your engine. That being said, a weak spark or any number of other problems could cause these symptoms. You indicate the T is a 1926. I'm sure you are starting it on battery. I've seen a poor connection at the switch act in a simular manor. So do this, instead of cranking her until she starts, start checking for a good hot spark before you go to start her next time. Check that each coil is "singing" to you. Or maybe you are running a distributor, if so check for a hot spark at each plug. Then move on to fuel. Crank her a few times and then pull a plug, is it wet with fuel. Is my choke working properly. Keep going in this fashion and you will eventually get it narrowed down to the culprit. Does or has anyone added a fuel filter? This usually sends a red flag up, at least for me. Why was a fuel filter added. Usually, or many times that indicates possible contamination in the fuel tank. See if you can have any luck narrowing your problem down some. Keep us posted.