Just with this app, and just on the Roku stick. As someone else says on the comments, it's extremely annoying and I don't even need to turn the TV off for it to ask for the cookie consent again, it's enough for me to navigate away to another app, and when I come back, it's there again.
I couldn't figure out how to message NOW TV support directly though, so I guess I'll live with this problem forever.
Email customerservices@ NowTV.com (without the space in).
While you are there, please remind them that they promised to fix the similar issue where Now on Roku does not pick up the Roku Subtitles (Closed Captions) options settings like it should, so I have to set subtitles on every time I watch a Now programme on the Roku.
Not that the subtitles setting is remembered on any other platform, of course, but there seems to be less excuse for getting it wrong on Roku devices.
I only got the Cookies message once on my Roku Stick Plus and when I opened the NOW App I navigated down to the bottom of the NOW App home Screen page and under the new Cookies Settings tile box (far right on the bottom grid row) I clicked on the accept all option.
That was about three or four days ago and I haven't seen the Cookies message since.