Uhmmm...
Compared with older vehicles, cars with S&S (as GK Jazz) generally have bigger and electronically controlled generators, able to recharge quickier the battery even at idle. Usually batteries are built with EFB technology (or AGM), so they can get more current in the first minutes after startup, and state of charge is closely checked by the energy management system. So I'm not so convinced that short trips are bad for your Jazz. I mean, very very short trips are bad, one, two, three minutes... But 3-4 minutes should be enough for recharge. Maybe I'm wrong, but I'm more worried about forgotting front interior lights on overnight than short trips.