It's not certain what prompted the rise in demand, although there are a few likely factors at work. Increased accessibility no doubt helps, as you're more likely to spend that $15 per month if you know you can watch HBO on your PlayStation or Xbox. Gradually increasing internet speeds make streaming a more realistic option. And of course, good programming is key -- the one-two combo of Game of Thrones and Westworld no doubt helped persuade some viewers.
As for extending the streak? Time Warner says it's planning to add more digital distribution allies to reach people who wouldn't normally see its marketing (think cord cutters and others who don't watch much conventional TV). There's no telling that this will be enough, but it's clear that the focus is shifting away from the novelty of internet-only HBO and more on its merits.