The CBS series is still slated to run on the network at least until September of 2019. The show, most likely, will even continue after 2019 as well given the recent ratings. Starting out in 2007 on CBS, Big Bang Theory was rated #68 among television audiences. With Season 2, the show saw a ratings increase going from #68 to #40, Seasons 3 and 4 saw an additional increase taking the show's popularity from #40 in the Nielsen Ratings to #12 and #13, respectively. Season 5 of Big Bang Theory saw the show become even more popular, no doubt, because of the show's syndication on pay cable networks. Season 5 saw the show's popularity increased from #13 to #8, Season 6 gave the show even more of an audience in the Nielsen Ratings when it jumped from #8 to #3, making it the third most popular television show on in the United States. Since Season 7 of Big Bang Theory the show has maintained its increasing popularity going from #3 in the ratings to #2 where it has stayed as of Season 10 which completed airing in May 2017.
With the Big Bang Theory consistently receiving an audience that makes it the second most-watched television series in the United States, it's highly unlikely that the hit CBS show with Sheldon, Leonard, Penny and the gang will be going off the air anytime soon.