I've just done a couple of tests with my placeholder app. Even though the question is closed, I was able to generate a new access token (following the regular procedure) for my sockpuppet account, and with it I was able to edit an answer in the Sandbox. The token for my regular account continues to work as well.
When the post is deleted, write access is revoked; you'll get an error message:
{"error_message":"Applications must have a registered Stack Apps post to write","error_name":"access_denied","error_id":403}
Read-only access (e.g. access to the user's global inbox) continues to work, and acquiring a new token is also possible.
P.S. if you ever decide to test this by deleting and undeleting your question, don't forget to re-add its URL to the application listing.