I get this a lot! Here is why:

(1) No 'Heavy' Gates at the airport.
The only fix for this to have the airport made with larger gates by a 3rd Party developer, or to use a program that allows you to make make larger Gates at the airport.

(2) The 'Heavy' Gates are not available because AI aircraft are using them all. I get this a lot because I use UT2, so my airports always have plenty of AI traffic, and if I can't park.
If you are only using default AI traffic, go to Options > Settings > Display > Traffic and reduce the airliner traffic.
If you are using UT2, then use CTRL+SHIFT+T to stop the traffic (mine restarts after about 5 minutes but it gives me time to be allotted a Gate by the ATC).
If you are using any other 3rd Party traffic, read the instructions to find out what commands might stop/start/reset etc.

Hope this helps.