"Always Send Cookie" problems?

Adding a oneconnect profile (I assume you already have an http profile) can help to fix that problem. By using oneconnect the client is not fixed to a backend server by a tcp connection, it will load balance the http requests individually so if in the same tcp session it sees different cookies with different persistence information it will honor that. Have a lookhere: https://support.f5.com/csp/article/K7208