Hmm, I take it back somewhat.
I don't know how it will behave in your scenario, but 2 seconds isn't short. I saw that my AP was answering to directed and broadcast probe requests in that time. After 1,2s it actually authenticated one client again and after 1,5s it sent a probe response and retried it like crazy. After that it answered some probe request again, put out some beacons and that lasted for almost 8s.
The problem might be that clients might think they can connect to the AP, however they will be denied each time. Maybe try just unplugging it 🙂