You can achieve part of your requirement using priority group activation with destination persistence.
1. Server A goes down.
2. Priority Group Activation kicks in and activates Server B to take traffic.
3. Server A comes back.
4. Due to Priority Group Activation Server A will start taking traffic as Server B will go inactive due to lower priority. So the persistent connections will stay on Server B, but all new connections will go to Server A. (Not sure of exact behavior, to be tested)
OPTION - 2
If you really want to keep Server B as active even when Server A is available, you can use a customized HTTP monitor with "Time Until Up" feature (for example, keep it down for 30 minutes) for Server A to keep it down for as long as you need to.
OPTION - 3
You need to find an external script or automation tool to monitor Server B status for active connections and change its Priority Group Acitvation priority to be more than that of Server A.
OPTION - 4
Trigger alert when Server A goes down so that you can manually login to the device and change the Priority Group Acitvation priority of Server B to be more than that of Server A.
Try out the scenarios in lab enviroment and you should be able to select the one easiest and most suitable for you.
Good Luck!
Regards,
Mohammed Mohsin