Hi Davy40,
Thank you for getting back to me with that information. Since you're connected via USB there's no reason you should be losing connection mid-print job, so I would first suggest making sure the cord isn't loose, or becoming loose either from the printer or the computer. If the cable is secure, please download and run the HP Print and Scan Doctor and it should hopefully be able to give some suggestions as to what the issue is that you're experiencing.
If the issue remains the same after these two steps, please get back to me with which version of Windows (Windows 7, Windows Vista, etc.) you're running and I will find something else for you to try :)