Car starting problems

The car starts easily when the motor is cold. If I park the car for 30 minutes and then restart the motor, the following happens:

1. Motor turns over

2. Motor stutters and stops

3. I press down on gas pedal and turn igition on-it starts with a little stutter

You may have a leaky fuel injector.

What year is your TL? How many miles on the car? What’s its maintenance history?

it is a '99 TL with 130K miles

And its basic maintenance history? Plugs & wires up to date? Air & fuel filters? Other things…?

The next time you stop for 30 minutes pull the vacuum line from the fuel pressure regulator. If you find any evidence of gasoline in there, replace the pressure regulator.