App Connectivity issue

I see that this post is a bit old, but for those who run into the same issue I will add a response.
I've worked with F5 VE in Azure quite a bit and have seen the issues mentioned.

Unfortunately the setup is a bit tricky, but explained well by F5 on their docs.

Firstly you should use the mgmt port as the health-probe port, so if that is 443 or 8443 use that as healthprobe for all LB rules. This has to do with how the health-probes function, just having a F5 VS with the port is not enough, so you should use the web-gui port. 

Secondly the LB will strip/drop TCP-RST and TCP-FIN messages which causes a bit of session mismatches, along with the 4min timeout. So go ahead and set the timeout to at least 5minutes on the LB rules and switch ON the TCP Reset function to actually forward those.

Further if you wish to have F5 VS on the same IP as the frontend-ip of the LB you need to switch on "Floating IP" on the LB rule. 
Natively the LB will change (DNAT) the destination address on the packets to the actual instance IP of the backend instance it forwards traffic to. This of course does not work well with F5, so to fix that the "Floating IP" will retain the destination address, but still forward it to the F5, which allows you to set up a VS with the same IP as the LB front-end IP. Note that you do NOT need to set up an internal interface with the IP or VLAN with that IP, just the actual VS. And the VS will pick up the traffic even when it comes in on an interface with another IP. (Just like on-prem). 

Hope this helps, please mark this as resolved if you think it helps, so that other users might find this as well!

Br
Kristoffer