Houston has been blue for a long time. The last Republican mayor was Jim McConn, who went out of office in 1982. Since then, we have endured the likes of Kathy Whitmire, Lee Brown, Anise Parker and now Sylvester Turner (who was ably supported in his mayoral bid by Sheila Jackson Lee). The city is a sanctuary city, so new democrats are popping up all the time.
Houston Republicans don’t seem concerned. They elected a weak chairman in 2014, and he is still there.
At least back in the day Texas Democrats were more conservative than the Rockefeller Republicans.