The problem is that something isn't working right. I'd fix that instead of add other equipment. If your RV is plugged into your gen. and while it's running your batteries are going down then your on board converter (charger) isn't working right.
If you're talking about a starting battery on a portable gen. going down while it's running then the charging circuit on the gen. isn't working right.
If this is on a MH and your saying the starting battery (and not the house battery) runs down then you need to find out why it's not charging. Some are wired to charge and some aren't. If your isn't then I'd install a circuit to charge it from your house batteries.