Well, from my "Why does everything happen to me" personal history files, I'll give you a weird possible cause for the no-start scenario when the engine is warm, i.e., after the Model A has been driven. But do check out all the other good suggestions posted so far first! The following is to be considered only as a last resort possibility - but it DID happen to me in 1974 in Germany. I wrote about this incident in my "Model A Trader" magazine column in the early 1990's, so stop me if you've already heard this
one.

I won't go into the whole story as it appeared in that magazine, but I will tell you what the problem turned out to be after exhausting all the usual tests. I took my 1928 Roadster to Germany with me to tour the country while I lived there for a year. Before leaving Arizona and driving the car to New York City (and personally loading into the cargo ship!), I changed everything that I thought might fail or that looked a little suspect. The original terminal box looked kinda crusty, so I installed a brand-new, shiny terminal box ordered from Rick's Antique Auto. THAT alone should have been a red flag. This was before the Model A community discovered what lousy junk parts were being sold by the now-defunct parts house.
Anyway, the car ran fine across country to New York and for some of the driving from
Hamburg down to Munich in Germany, although I was deluged for three days straight by liquid European sunshine, to be read: "RAIN!!!". The engine ran well each morning, but after a while, it misfired and wouldn't start when I coasted to a stop along the Autobahn, mostly making it to rest areas for repairs. The danged thing would not start for about 20 minutes, no matter what parts I swapped around. And then almost like clockwork, the car would start and be fine for another few miles before it began to miss. Cutting to the chase here, I removed my brand-new shiny Rick's terminal box from the firewall and found the problem. There, beneath one of the two long round-head bolts were signs of electrical arcing. The slotted roundhead bolt installed in that Taiwanese terminal box was way too big to fit down inside the hole in the terminal box for it. It's head was sticking out just enough to allow arcing when the firewall got hot after driving for a while. While the car sat and wouldn't start, the firewall had cooled and contracted, creating enough of a gap between it and the round head of the terminal box bolt to allow the car to start and run well until the firewall got hot again after a while driving, and expanded to cause the arcing again. While the engine was running, it misfired. When I shut the engine off, it wouldn't start for 20 minutes. Apparently while the engine was running, the ignition system still functioned, although with a miss. By shutting off the engine, it wouldn't start. It was undoubtedly shorting out.
To fix the problem, I don't recall whether I filed the head smaller or put rubber
between the bolt head and the firewall. Anyway, that solved the problem and the car ran fine for a year until I sold just before returning to the States.
A once-in-a-lifetime occurrence, you say? Nope! The same thing happened to a friend's 1930 Coupe in the 1990's and a friend's Fordor here in Iowa 10 years ago. Guess what the problem was? That same &%^#%&* cheap-*ssed Taiwan terminal box with the wrong-sized bolt head! Rick's must have sold a ton of these lower priced boxes in the 1970'-1980's because I still come across them on older restorations. If your Model A's previous owner/restorer shopped with his wallet instead of his brain, your car probably has one of these worthless (but shiny!) terminal boxes.
As I say, it's a weird cause, but it definitely ruined the first week in Germany for me!
Marshall