Some things to check:
1. The air superiority required is over the air region you intend to drop the troops into, not the one they are taking off from.
2. The transport planes need to have enough mission range to reach the target. Check to see that in air mode the transports don't have a warning like "x airwings do not have coverage". Sometimes the troopers say all is well, but the transports disagree.
3. Make sure everything is at the airport, the transports and the troops, and that all planes have actually arrived. Also make sure the planes are NOT assigned to the air region.
4. Make sure that airport is in primary supply (supply route back to capital) with no shortages.
5. Make sure that all para divisions are in the same army with each other and that all are assigned to the battle plan. Sometimes if you had to move one of them to meet the others at the airbase, the latecomer is not assigned to the plan even though it looks like it should be.
6. If nothing has turned up so far, reset the orders and then save the game. Reload. If no joy, quit and reload again.
Oh, one more thing that believe it or not does occasionally trip people up: make sure you are at war with the nation you are about to paradrop onto. Example, as Germany make sure you have already delivered and then gotten the "newspaper" event about your declaration of war on Denmark before trying to paradrop on Odense.