Some of what I'm going to suggest is the obvious, because it isn't always.
First, make sure iTunes is authorized on your computer. This has to be the same account that your iPad was set up with. Go to the Store menu and choose authorize computer. It probably is, but if I remember right is is possible to buy content on an unauthorized computer, so maybe it isn't.
On the iPad, go to he Apps Store and scroll to the bottom of the Featured Apps page. Make sure you are logged into the same account that you bought the apps with.
With your iPad connected, select it in iTunes. Now tap on the Apps tab at the top of the screen and make sure you have your Apps set to sync. Make sure that all the apps you wan to sync have a check mark next to them in the list to the left.
If you want apps that you buy on the iPad to automatically be synced back to iTunes, also select the auto sync apps. . . (whatever it says) just below the list of apps.
Some of these steps may not be necessary. I'm just suggesting some of the things I would try if it were my problem.