I have an app in the app store and the distribution profile is about to run out in about a week, but my developer membership doesn't actually expire till next year. Do I need to rebuild and re-submit my app with a new certificate?
You can renew the certificate by selecting the certificate and clicking Renew. This means you won't have to resubmit the app just to update the certificate.
The certificate is only required for submitting the app to the store. If you wish to update a new version or another app, you’ll need to renew the certificate in the Member Center.