Which PIR sensor.
Common HC-SR501 PIR sensors don't need pull up or pull down.
You should adjust the "time" pot fully anti-clockwise (and leave it there).
Otherwise you might have to wait up to 7 minutes for the pin to go LOW.
(any movement could start another 7minutes).
If the pot is fully anti-clockwise, the PIR output should go LOW in about three seconds.
Now you can control time delays with code.
Leave the "sensitivity" pot in the middle (it does not adjust sensitivity).
Post your code (with code tags) if you're still having problems.
Leo..