monitoring server sees Internet routers as down after connect F5

it is a guess, but i can imagine that the F5 is sending the traffic to be routed by the router further and that the telnet and other monitoring isn't picked up by the router as such and gets lost there. or even that because of the load balancing the traffic is send to another router then the one you want to manage. can you reach the routers from the F5 fine?

do you manage the router on the same address as you send the routed traffic to? is it possible to manage the routers via another network / ip address?

(off topic: dont use telnet, use ssh)