That's very similar to a problem I have. When I do hit on a winning trade I close much too early for the most part.
While I'm waiting on my long term trades on the live account, I may experiment with the demo account. I do terrible during volatile times but maybe during quiet times with no news I can do better picking up a few pips here and there.
I've gotten very gun shy lately though so I doubt if I'll do any live scalping. Probably just kill time with the game account for kicks.