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Is there a mysterious one way valve somewhere along the fuel system ?

Replaced fuel pressure regulator, both pumps. Not sorry, they were thirty years old or looked it. Still, my '79 fires right off no matter how long between starts. '81 takes ten or more turns to fire after sitting a day.

Just seems like the fuel has gone back to bed.

Short time, like in and out of a store, it fires right off. No smoke or signs of flooding.

I had the exact same problem,in my case was the cold start injector not working due to the sensor that actuates it , this is the one at the thermostat housing.
Try to cranck in the morning when stone cold, with the start injector off the intake and see if you get a squirt of gas.
Remember the engine has to be cold.

Wil is correct, the Thermo-time switch controls the CSV. No worky, no squirty. It lives right next to the coolant temp sensor in the thermostat housing (and looks a lot like it).

There is supposed to be a check valve in the fuel pump. Seems like I read about a TSB one time for E23s where they put in an external one due to problems similiar to what you are having, but why only on them when E12s, 23's, 24's and many E30s used the same pump?

What does it run like when it does start? Is it fine, just like it should be or does it take a little while like it has to clear it's throat? Leaky injectors can flood it and cause an excessively rich start up condition. Any smell of gas out the exhaust?

Thanks to all, now I have a checklist.

I'm taking the car to a full shop friend to play with the computer / sensor / exhaust gas toys. They have an industrial injector cleaner. Free or trade for, so I don't care if it's snake oil. He's a straight shooter and swears by it.

To the point, it runs gang busters after initial flubby warm up. No smoke just after start, I can tell it's a 56,000 engine as opposed to my 120 '79.

New O2 sensor going in, then sensor swaps as suggested. *#@! bugs will be remedied and solutions reported.

There is a way to check your sensor and your cold star injector, individually
If you will like to do that

Check your grounds. My M535i was very hard to start. It would take 10, maybe fifteen tries to get it to start. Now it fires up immediately.

Not saying it's your problem, but take a looksee to rule it out.