I’d perhaps make this a configurable option for the forum admin. Might be something that could be disabled, perhaps give the option of a timeout? If person tries to delete within a few minutes/hours (as configured) that’s fine.. but if it’s a few days later then the option disappears.
If someone can post and delete immediately it could be used as a mechanism for antagonising the original poster, especially if they receive a notification of a reply. Might also be worth adding a configurable limit? User can delete n number of their own posts per day?