Well, this was inevitable. After scathing reviews from critics and a thumbs down from fans, Paramount tried to fight numerous reports that the planned sequels to "Terminator Genisys" were on hold, with producer Dana Goldberg saying last fall they were "re-adjusting." Well, it looks like they re-adjusted the followup right off the release calendar.
The studio has pulled the followup to the franchise reboot off the schedule, and instead, put the Dwayne Johnson starring "Baywatch" in its place on May 19, 2017. That movie has Dwayne Johnson leading an R-rated take on the corny '90s series, and my guess is that Paramount realized they'll probably do much better to put their dollars on that project, rather than trying to keep 'Terminator' active.
So what's the future of "The Terminator" franchise? Well, the North American rights will apparently revert back to James Cameron in 2018 (though, that was the case years ago, and who knows if that has changed). But it's probably safe to assume that if that's still the case Cameron, who has been somewhat unhappy to see the franchise continue without him, probably will hang onto it, if it falls back into his lap.
Meanwhile, Sony has pushed back their "Jumanji" reboot from Christmas Day of this year, to July 28, 2017. Glad to know in case you had big plans to see that movie during the holidays...