HA Connection lost after change Management IP address

I would suggest you read how to setup HA in V11. It is no longer really a HA Pair, but a cluster. This may give you an idea of what all changes you need to make in order to get this working in V11.

https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/bigip-device-service-clustering-admin-11-4-0/3.htmlunique_2103230074

One thing to check for is your trust list on each device. From the above link you need to see what you have configured under " Device Management > Device Trust, and then either Peer List or Subordinate List"

You trust the management IP address of the other devices in the cluster. So if you are changing the management IP address, you need to update the trust list.