Unable to connect/RDP/SSH to the failed over virtual machine
Is Connect button grayed out on the virtual machine?
If your Connect button is grayed out and you are not connected to Azure via an Express Route or Site-to-Site VPN connection then for ARM (Resource Manager deployment model) add a Public IP on the Network interface of the virtual machine as shown below.
Is Connect button available (not grayed out) on the virtual machine?
Check Boot diagnostics on your Virtual Machine and check for errors as listed in this article. Note: enabling any setting other than Boot Diagnostics would require Azure VM Agent to be installed in the virtual machine before the failover
If the virtual machine has not started, try failing over to an older recovery point.
If the application inside the virtual machine is not coming up, try failing over to an app-consistent recovery point.
If the virtual machine is domain joined then ensure that domain controller is correctly functioning. You can do that by creating a new virtual machine in the same network and ensuring that it is able to join to the same domain on which the failed over virtual machine is expected to come up.
If the domain controller is not functioning correctly try logging in to the failed over virtual machine using a local administrator account
If you are using a custom DNS server then ensure that it is reachable. You can do that by creating a new virtual in the same network and checking that it is able to do name resolution using the custom DNS Server