I remember the rumour that the reason Saavik stayed behind on Vulcan in The Voyage Home was because she was pregnant with their baby after she helped him through his ponn farr in The Search for Spock, but that's the only thing I can think off hand.
I remember reading about that rumour in some book about Star Trek 4. I also seem to recall that Peter David did something with the rumour in #76 "Captain's Daughter", but it's been over ten years since I read the book.
But I seem to remember that it came about because of the Ponn Far scene in STIII (when Spock was a teenager), and people thought that because Saavik was the only other Vulcan on he planet, Spock and Saavik---ah----did it. And that Saavik did conceive and it was the reason why she didn't time travel with Kirk and crew (plus from a budget point of view, the film makers probably were trying to save money and come up with an excuse as to why Saavik was separated from Kirk and crew, even though she should've been sent off for debriefing before the movie began, and Kirk and crew arrested).