Why can't I transfer purchases from my jailbroken iPhone 3GS to iTunes? I have a jailbroken iPhone 3GS and I cannot transfer purchases to iTunes.

This is a recent issue; I could transfer purchases earlier.
If both iTunes and the iPhone are logged into the same iTunes account and you still can't sync the apps and you don't want to play with the iPhone too much (jailbreaking does weird things sometimes, seemingly irrelevant stuff can break things), you can just download the apps again in iTunes. All purchases can be re-downloaded for free.