It does not affect responsiveness. It just tells asterisk to wait up to X time before disconnecting a rogue or unresponsive manager connection. The fop2 server performs ONE asterisk manager connection and keeps it up all the time, to receive events and send commands. If that link breaks, then you will loose events that will ultimately update the FOP2 web display. If the manager disconnects every now and then and it is not stable, then FOP2 won't be stable either.
Also, be sure to use always the latest available FOP2 version, what is the one you are using now ?
/usr/local/fop2/fop2_server -v
To find out.