Looks like this question was from over 10 years ago so it is unlikely they will respond.
However, if you are having the exact same issues the likely cause is a crank sensor issue.
Here is a guide that will help with this:
https://www.2carpros.com/articles/symptoms-of-a-bad-crankshaft-sensor
Basically, the sensor tells the rest of the ignition system when to fire the plugs. When it fails it can take a little time before it allows the engine to start again.
I attached the info from the manual that will help with replacing it. Clearly this is a guess at this point so let us know any other details that you have on your issue.
If it is a different vehicle then listed above, we should get a new post started.
https://www.2carpros.com/questions/new
Please see the info attached and we can go from there. Thanks
Images (Click to make bigger)
Thursday, February 17th, 2022 AT 5:12 PM