I don't think this problem would be caused by iTunes. If it's something related to iTunes, it would likely be caused by the iTunes library. You can do a test with another iTunes library on the same computer, by creating a new user account (on your computer). I don't know if you use a Mac or Windows PC, but you can do so on either system, and when you log in to the new user account and run iTunes, you are using a different (new and empty) iTunes library. You can add a limited (but large enough) number of songs to that iTunes library, and try syncing your iPod as a test. If it works properly in the new user account, there is no problem with the iPod. If the problem recurs, the cause is likely to be a problem on the iPod. That will help narrow down the actual cause, instead of trying random things, especially something that's a lot of work, like transferring everything to a different computer. If the problem is on the iPod, the same problem will occur.
I don't know what model iPod you have, but if it's an iPod that uses a hard drive for storage, the cause may be related to the hard drive. Hard drives can become faulty in a way that does not allow reliable storage of data, although it can go through the Restore process without error. What may be why it prompts you to do a Restore, when you connect it.
One thing you can try is to erase (reformat) the iPod using the system, not iTunes. If you use a Mac, you would do so using Disk Utility. I don't recall the specific command or tool in Windows, but it's the same thing you do to erase (reformat) an external hard drive or USB flash drive. iTunes should NOT be running when you do this. If there's an option to do a "quick format," select to do a FULL format. If the iPod's disk is not mounted by the system when connected, use the procedure to set it to Disk Mode first
Putting iPod into Disk Mode
If there is a problem with the iPod's hard drive, it's possible for it to fail the erase (reformat) procedure. If it succeeds, run iTunes and do another Restore. It's VERY important that you do a Restore, because after being erased outside of iTunes, it no longer has its onboard software and setup. After the Restore, try syncing it again.