One thing I haven't seen brought up in the way of explanation would be the prohibitive costs of licensing the likenesses of Harrison Ford and/or any of the supporting cast for an animated series. Originally, Amy Adams' Giselle from Enchanted was going to be a Disney Princess until Disney decided they didn't want to keep paying her fees to license her likeness for as long as the Disney Princesses stay in circulation. Harrison Ford is so inexorably tied to Indy that you really can't do a show with him without needing to license his image. This was probably prohibitively expensive back in the day, and would be even more expensive to do now.
The idea of doing "Indiana Jones, Jr." also doesn't sound like much of a winner to me. In return for losing the lead character and the more lurid aspects of the original movies, you get a kiddified show that won't satisfy anybody. I don't recall James Bond, Jr. being anything more than a moderate success, and that result might have discouraged a comparable Indy Jr. series. The new movie also presents a problem with that because you either break with continuity or have to license Shia LaBeouf.
The Indiana Jones Adventures comics might be a step towards changing that, but I wouldn't get your hopes up. Personally, if they did do more Indy, I'd prefer something akin to the Hellboy Animated route, with DTV animated movies. However, judging by the new movie and the presumably tepid sales of Hellboy Animated, I doubt anyone would think an Indy DTV animated project would do well.
One of these days, I'll figure out how image licensing rights work for sure because I'm curious about it myself. This might also explain why there hasn't been an animated series spinoff of Pirates of the Caribbean -- up front, I don't think anybody at Disney (or outside it) was expecting the first movie to do as well as it did, so I don't think anybody thought to even ask for image licensing rights. I expect that the major players in the Star Wars prequels had likeness licensing for toys and animated spin-offs as part of their contracts because it IS expected that Star Wars will generate toys, cartoons, video games, and all that other cool ancillary stuff. However, that might be why there have never been SW cartoons set in the original trilogy timeline. Video games have a built-in shelf life, but a successful cartoon can circulate via home video and syndication for decades. Even then, you ever notice how Han Solo almost never shows up in those video games?
-- Ed