When searching for advice on this in 2021, I couldn't find anything useful on the NOW TV Community Forums or elsewhere... So I've noted it here.
NOW TV won't Pause
TL;DR: Do a factory reset
I only use it for Sky Sports F1; I can't speak for any other uses of NOW TV, but I assume it would be the same.
The initial behaviour was that the NOW TV stick was able to pause live TV for around 30 minutes - it has to store all of that data internally, so obviously there is a limit, after which it starts playing again, from the point at which it was paused.
The problem I found was that it started to misbehave. It would pause for a few seconds, then immediately resume playback. This is no good at all, obviously.
Most such devices typically have a fixed (read-only) storage area with their basic firmware, and a second storage area which can be read but also written to. This second storage area will store your personalised settings, its ongoing note of its current state, and would also be used to buffer the TV stream which has been broadcast but which you have not watched yet. So a suitable hypothesis is that it had somehow ended up writing a load of junk to this storage, and ended up in a situation where it didn't have any space left to actually store your paused TV stream. I don't know what junk it got filled up with, it's obviously poor management of its systems, buffers, logs, whatever... I didn't bother to investigage, I'm not one of those people who can reverse-engineer such a device, even if I did have the time and inclination to do so. But if that was the situation, then it stands to reason that there's going to be a "factory reset" facility, and that that would wipe out all of that storage, to put the device back in its original situation.
So, what I did, and this may not work for you, but this did work for me, was to follow the How to reset your NOW Box or Smart Stick article on NOW TV's website. And it worked.
For the Stick, the instructions are (whilst the device is powered on) to hold down the small reset button at the opposite end to the HDMI connector.
For the black Box, it looks like there's a RESET hole which you'd need to hold a ball-point pen (or similar) in for 30 seconds.
For the Smart Box, the reset button is apparently on the underside, and needs to be held in for about 6 seconds.