I don't know if he exactly lost the rights or anything, but I know the first was a big passion project for him. Reading interviews, it sounds like he was set to direct the sequel, but the studio didn't bother booking the sets he wanted, and then tried to move things to China afterwards against his desires, so he walked.
I dunno, considering the poor reception to all the sequels, if the studio wants this to be a big franchise, I'd be throwing money at Del Toro to come back.
Would the prequel be when the first Kaiju rift opens? Or maybe in the universe where the kaiju's come from? I think I'd really like to explore that universe