If you have an Open Asylum, however, anyone you remove from the asylum can re-join. If you allow posting access to all members, as well as the Open Asylum option, anyone whose posting access you remove can leave the asylum and re-join to get posting access again.
To prevent a member from re-joining an asylum, you can ban them.
-- Banning a user
To ban a user from an asylum, you must be logged in and go to the Admin Console [http://www.insanejournal.com/admin/console/]. You will then need to execute the following commands, replacing "asylum" with the username of the asylum and "user" with the username of the user. Be sure to remove the quotation marks when executing the commands.
The following command is to ban a user from your asylum: ban_set "user" from "asylum"
The following command is to unban a user from your asylum: ban_unset "user" from "asylum"
The following command is to list the banned users of your asylum: ban_list from "asylum"
Banning a user from your asylum does not remove their membership, but it does remove the ability to comment and post into the asylum. However, if you remove and also ban a user, they will not be able to re-join.