I've just done a couple of tests with my [placeholder app](https://stackapps.com/q/8039/34061). Even though the question is closed, I was able to generate a new access token (following the [regular procedure](https://api.stackexchange.com/docs/authentication)) for my sockpuppet account, and with it I was able to [edit an answer in the Sandbox](https://meta.stackexchange.com/posts/327624/revisions). 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](https://api.stackexchange.com/docs/inbox)) continues to work, and acquiring a new token is also possible.