I have the same issue on a Galaxy Tab A running Android 7.1.1.
By the sounds of it, NOW have no intention of sorting this as it's been going on so long by all accounts, No way I'm doing a factory reset (which sounds like it's only a temporary fix anyway) so I'm afraid to say this is the end of the road for NOW TV. You don't get this crap with Netflix.
I am having same issue on two identical Lenovo tablets and know of two other people with the same problem. The issue only started after the last app update, I believe mid October 2019. Trying to get any reasonable help from Now TV technical staff is almost impossible.
I have a Lenovo Tab 4 10 running Android 7.1.1. To resolve this issue I had to factory reset device using the hard reset option. Re-installed NowTV app, and now playback restored. Hard reset option accessed from powered off state by holding both power and volume-up button till menu comes up. Detailed at URL https://www.hardreset.info/devices/lenovo/lenovo-tab-4-10-wi-fi/hardreset-first-method/
Alas as previously reported, factory reset is but a temporary fix. Getting signed out again on payback. I have a Lenovo Tab 4 10 Plus, which Lenovo released knowing they were unable to update Android on, so cannot get around this issue unless Sky/NowTV got their finger out to fix whatever their app issue is with Android Nougat 7.1.1
There appears to be a bug in the NowTV device registration process with Android Nougat 7.1.1 devices. If you experience 'you have been signed out' error when trying to play content, see if your device is actually appearing on your account (my devices). If not, there's the issue! I reported it today to the chat support people, and they said they'd report it to Tech support, but judging by previous chat interactions, no one gets any further contact from Now TV support. I will be pestering [email removed] if so don't hear from them in couple of weeks.