Idle problems after car is warmed up @ start.

[abregopaco]

Hello everyone,
I hope you can all help me with this. In the morning i start the car, this is the first time my car is getting turned on and it's been sitting overnight. It starts fine and it has no problems. Now my problems start happening on my second start, after it has been warmed up. For example, if I go to the store (at this point my car is fully warmed up) and shop around 15 to 20 minutes. When I go to start my car the second time around it has a low idle and it feels like it wants to turn off. This happens for about 5 seconds and then it goes back to normal 750 to 800 rpm. After that the car runs fine until the next start. This only happens at start and when the car is warmed up. It's been happening for a month now. My car is a 97 Acura Integra LS, MT. I have replaced the following.

Spark plugs ( 11 months ago).
Spark plug Wires ( 1 month ago).
Idle Air Control Valve (2 days ago) I thought it was this.
Distributor with rotor and cap (2 Months ago).
Oxygen Sensor from headers (1 month ago).
Compression is fine (tested 1 month ago by mechanic).
No coolant in engine (tested 1 month ago mechanic).
Engine coolant temperature ( tested 1 week ago).
Tested the fuel pressure visually (2 months ago).
Radiator replaced with all water hoses (3 months ago).
Full timing belt kit (water pump, all belts, seals) (4 months ago).
I check the vacuum hose that are relevant. I don't know exactly where are all of them.

Any suggestions or should i start looking for a new car. lol

[Teggyxlove]

Could be an alternator

[Hondacuraplanet]

Try this.

Before starting the car under conditions that would cause the issue, turn the key to the RUN position for 5 seconds, then off, then back to run, then off, then start the car. I'm curious to know if the issue is related to a drop in fuel pressure. If so, the car will start and run normally at that point.