I think a good starting point for anyone coming across this thread looking for help with their iphone continually connecting/disconnecting from Windows itunes would be:
Set itunes to not start automatically when the iphone is plugged in...if the iphone can retain the connection to the PC when itunes is not running then it would suggest some sort of itunes software glitch. If the problem remains with itunes not running then it would suggest a USB related issue.
If feasible see if the iphone will sync when connected via another pc.
Remove all other USB devices and see if that helps.
Try all the USB ports.
Check for updated USB drivers for your motherboard.
Buy/borrow a plug in USB pci card to try.
Buy/borrow a powered USB hub to try.
The big power draw when the iphone is plugged into the USB port is in recharging the battery...so try fully charging the battery off the mains before plugging into the USB port.
May I come with a slightly different route?
Shouldn't one start with re-installing the software? I mean it is recommended on so many places. And also, I think its better to try with a USB hub before trying to a new PCI card since it is probably more easy to borrow.
1. Make sure that re-installing iTunes does not help.
2. If possible try to sync or transfer files to your iPhone from another PC, to make sure that your cabling and iPhone is flawless
3. Try to remove all other USB devices and see if that helps.
4. Try all the USB ports while having all disconnected
5. Check for updated USB drivers for your motherboard.
6. Buy/borrow a powered USB hub to try.
7. Buy/borrow a plug in USB pci card to try.
Also one comment about testing to not keep iTunes running. Atleast on my HP machine(not a HP MC but ordinaray desktop) there is no problem what so ever when iTunes is not running, its only when syncing with iTunes, iTunes thinks it got disconnected(Windows still has it connected). The only way to get iTunes to realize it is actually connected is to re-connect the iphone.
Regarding choosing USB PCI card, I realized that the card I bought with a VIA chipset didn't work very well with my HP machine, though the second one I bought, with a NEC chipset has worked flawless.