Many would likely put Indiana Jones and the Last Crusade at the top of the popular franchise and a large part of the reason for that is the great chemistry between Harrison Ford and Sean Connery. The fact that we would not see this again in Indiana Jones and Kingdom of the Crystal Skull is just one of the many disappointing things about the fourth installment in the franchise. It turns out that we could have seen Connery reprise his role as Henry Jones, but back in 2007 the retired actor explained why he passed on appearing in the most recent entry, there just really wasn't that much for him to do. According to Connery...
I spoke with Spielberg, but it didn't work. It was not that generous a part, worth getting back into the harness and go for. And they had taken the story in a different line anyway, so the father of Indy was kind of really not that important. I had suggested that they kill him in the movie, it would have taken care of it better.
Steven Spielberg apparently took Sean Connery up on his idea, as the only reference to Henry Jones in Indiana Jones and the Kingdom of the Crystal Skull is to remark that he has passed away in between the events of the third and fourth films.
An interview that Sean Connery gave back in 2007 has recently resurfaced online where the actor makes it clear that he has little interest in returning to Hollywood. Connery has been very public about his dissatisfaction with the production of The League of Extraordinary Gentlemen, the 2003 film that was Connery's last on-screen role. While the actor has done a little voice acting since then, we haven't seen him in a movie in nearly 15 years. He at least entertained the idea of coming back in 2008 for the last Indiana Jones movie, but it sounds like the part may have been little more than a glorified cameo, and to him, it just wasn't worth it.
Of course, in hindsight, most fans probably wish that the script for Indiana Jones and Kingdom of the Crystal Skull had been rewritten to give Sean Connery a bigger part, a film that focused on Indiana Jones and his father might have turned out much better than the movie about Indiana Jones and his son that we got. Crystal Skull is not looked upon fondly by critics or fans. Perhaps the creators should have taken Connery's lack of interest as a sign.
Sean Connery says in the interview that he doesn't see that there's really anything that would cause him to come back to movies, and he's remained true to that sentiment ever since. Of course, since they killed off Henry Jones, it seems that even if they could talk him into coming back, there's no place for the character in the fifth Indiana Jones movie that is currently set for release in 2020.