As far as I'm aware (i.e. it would need to be confirmed by DAZ), the auto-renew feature is related to the monthly billing, not the PC membership itself.
You must of course enter the relevant information in the PC Payment part of your account (unfortunate that DAZ didn't really warn about the upgrades to the account page. Personnaly I found out when I bought some stuff and went to my account).

So, if you have been a member for a year (as displayed in the screenshots), what is displayed is the current billing method applied. Annual subscription, as originally offered, were 'converted' to monthly membership automatically (new version of the subscription), with no additional payement made (despite the 'renew' option, the system knows that the whole subscription was payed).

Now that the end of the subscription is reached, you must explicitly renew the subscription (either paying for the whole year in one step or choosing the monthly payments, and this option then activates the 'auto-renew' feature which bills you monthly).

I 'bought' a monthly renewal and the system seems to work (my membership as been extended for one month and I got a load of stuff as bonus).

The way the subscription works isn't clearly explained, though. I deduced most of the above explanation by watching how my own subscription behaved. I might be wrong, so the official explanation should be asked to DAZ.