serious problem with membership

I have membership setup with 6 subscriptions and 1 level. I have 2 finite subscriptions that do not recur and the other 4 are monthly, quarterly, semi-annual, yearly and they are serial.

The problem is the recurring (serial) subscriptions are not behaving the way the i expect them to. The first monthly subscription expired yesterday. The 2nd month payment was received in 2checkout and nothing seems to have happened in the Membership. When i checked phpmyadmin, the subscriber still had the old expiry time.

Is this normal? What happens if payment fails, the subscriber will continue to have access?