I had a feeling this will be the answer.
I know that decrypting WiFi WPA encrypted traffic when 4-way handshake is in the traffic dump and when passphrase is known is a trivial task. However, what about decrypting WPA traffic when 4-way handshake is not available. I have the SSID, I have the passphrase, I have messages 3 and 4 (I know it is useless) of the 4-way handshake. Is there a way of decrypting the traffic?