The live TV feature of Hulu has been pretty atrocious as of late. I really only have live TV for sports, and I (along with others from looking a Hulu's Twitter) have experienced playback issues during TNF, SNF and last night during the WS and NBA opening night.
I hate to say this, but AT&T TV Now live TV feature was more stable than Hulu. Although I refuse to go back to them, if the issues with Hulu persist, I'm going to have to look at YouTubeTV or PS Vue.
I doubt ATV+ will have live TV anytime soon. I could see them potentially adding the feature down the line, but for now, just look at them to be similar to Netflix, Amazon Video, etc.