I had never had it for a while, then started seeing it but never got around to asking, currently have forgotten to pay attention, and am now curious....and can see it now under certain circumstances. Definitely not in private browsing mode.
Iphone 7+, 12.4.1, Safari
* Refreshing an existing AP "tab" or instance or whatever they are called on Safari mobile: fine, is logged in.
* Using my shortcut button (the kind that look like an app), it goes to AP unlogged in, logs in by clicking log in (don't have to enter anything, just click log in). shortcut appears to go to: www.ar.attackpoint.org
* Using the + button in safari (between private and done) and selecting one of the AP instances in the group of frequently visited sites: arrives logged in
* typing in attackpoint.org
in the address/search bar ends up not logged in, logs in with clicking login (no typing anything, just clicking login)
* Chrome on Win10 always seems to arrive logged in