Safari isn't retaining cookies (and/or passwords) for some reason
1. Check that you're not in 'Private' mode. (Open Safari, tap on the multiple tabs icon [furthest to right], and make sure 'Private' is not highlighted)
2. Go to Settings > Safari > Passwords & Autofill and ensure that 'Remember Passwords' is selected.
1 again (although, obviously, you're seeking to turn Private Browsing 'off', not 'on' if that's what's actually required):
https://support.apple.com/en-gb/HT203036
In which case it could be that AB's server isn't always 'seeing' the cookies sent by Safari. I've been getting quite a lot of 'timed out' messages on AB today, so it does seem that AB's servers might be playing up.