Now, I tried with my computer and I had access to my account after just one verification session, but my phone has not passed verification ever since.
You mean that you haven't ever passed the cloud flare verification using your mobile phone?
To be honest, I navigates the forum mostly these periods using my phone and with the couple of times the forum website had required me to pass the security process before I can have access, it goes very smooth at my end with my phone.
So I'm probably suggesting that the error at your end was from your phone IP or browser.
You can also consider network error as the problem. You never can tell if the network was too weak for the activation when you tried doing the verification with your phone then the network grows stronger within the short time you switched over to your PC where the verification task was made successful.