Users having to manually reconnect RDP sessions

The 'Action on Service Down - Reselect' did not work. When the customer reloaded one of the RDP Gateway servers remote RDP users were disconnected and had to reconnect and sign in again. Looking at the article below is says that the 'reselect' option is only appropriate for 'transparent pool members, such as firewalls, routers, proxy servers, and cache servers'. My pool members are RDP Gateway servers of which a TCP 3-way-handshake needs to be established.

https://my.f5.com/manage/s/article/K15095

These RDP sessions use https/http and udp connections. The article says the below about failing over http sessions to another pool member so I'm not sure http sessions can be failed over to another pool member without the TCP session having to be re-created?

Note: Services such as HTTP require that the system establish a transport layer connection before transmitting HTTP messages. This is commonly referred to as a 3-way handshake, and is used by the client or server to establish communication options and to track requests or responses. When a server receives a request from a client without having established the transport layer connection, normal behavior is for the server to reject the connection by sending a TCP response with the RST flag set.