Although most of these are unlikely on a phone, here are a couple other possibilities for getting the cloudflare all the time instead of once per session.
1) Most sites that track if they have shown you something so it is only shown once per session do so with cookies. If you are blocking cookies or have software that auto deletes them, this could potentially cause you to keep being checked. I haven't tested this too see if that would cause the issue with cloudflare, but it seems likely.
2) If you are using any kind of anonymity software to mask out change your IP, this could be the cause as well. If your IP changes within a session, it could trigger a new check. Or, if your IP is known to be a fake one used by such software, cloudflare may check every time just to be sure you aren't causing trouble.
3) A third possible cause could be that you are located in an area (based on IP) with a high percentage of hackers, DDOS attacks, etc. and cloudflare is checking every time to be sure you aren't a problem.
4) If you use a VPN, it is also possible that cloudflare could be keeping a closer eye on you.
Or, 5... They know exactly how much trouble you are on this site and are targeting you on purpose. 😁