membership not updated with recurring contribution
Payment Processors do not care what the monies are used for. Once the transaction is completed the payment processor’s job is done.

You’ve either run into an issue with CiviCRM Core or with Webform CiviCRM. 

Issues with Memberships not renewing are (unfortunately) not uncommon. Membership renewals are complicated from a logic/code perspective as there are so many different Membership models already in core (rolling/fixed, statuses config). If Membership is important for your org consider an extension that handles the logic for you. Eg -> if Contribution is Completed -> add +1y to current Membership start (or end date) - whatever your rules are you have control.