iPhone 3G refuses to transfer purchased apps to iTunes

You can eventually attempt to transfer your iPhone apps to your iTunes library via CopyTrans (no jail-breaking needed as far as I know). After the transfer sync your iPhone with iTunes and see whether the issue is now fixed.

I'd seriously consider a hard reset of the iphone, reinstall 3.1 and let it sync from your itunes backup.

"In your question you have said that you restored your phone from backup.

I am guessing that when you restore the backup, it is restoring the problem as well.

I think that this type of problem should be able to be solved by restoring your phone and setting it up as a new phone and then syncing everything across to it.

Having said that, I am not sure what will happen with your purchases when that happens.

If, after that, the problem still occurs then it is time to contact apple for a warranty replacement."

"Have you tried to ""Reset all warnings"" when right-clicking on the iPhone icon in iTunes, then synchronise again ?

I also got problem when synchronising my apps with my iPhone and I found that I'd clicked one time on a option like ""Do not transfer applications & do not ask again"".
The problem was not exactly the same, but I hope this might help."