The few prognostications available show it remaining out of reach. Nate Silver has nothing new that I could find, but Larry Sabato is on the case.
Last updated Oct. 20, 2016. Current outlook: Democratic gain of 10-15 seats, short of the 30 net seats they need to gain to win the House.
You can use 270towin.com's map to go granular and fiddle with the numbers. The best-case scenario for the Blues that I could come up with is 232 R and 200 D (there are three House seats awaiting a special election after November to be filled.) Sabato's projection above matches mine, and has those vacancies blue for a fifteen-point swing, still short of Democratic control by the same number. So the Dems are only halfway to the count they need to take the gavel away from Paul Ryan and give it back to Nancy Pelosi.
Could it get better for them in the remaining two-and-one-half weeks before Election Day? Does Trump have any more suicide bombs to detonate? Could the Republicans retreat and retrench using the 'block President Clinton' maneuver? We'll just have to wait and see, but I'll go ahead and predict that the House stays in conservative hands.