the machine appears to reboot, but all connectivity is lost.
It is by design behavior. Before capture a VM image, we should use sysprep to generalize the VM, generalizing a VM removes all your personal account information, among other things, and prepares the machine to be used as an image.
After we run sysprep, we will lost all connection. Run sysprep, we should select shutdown:

For now, we can't via Azure new portal to capture a VM image. We can use PowerShell to capture a VM image, we can refer to this link.
you could create a virtual machine from an image. I can't find the
same function in the new portal.
We can't use Azure new portal to create a VM from image, we can use PowerShell to create a VM from image, we can refer to the link.
Most important:
Before you capture a VM image, you should back up you VM's VHD first, because the process will delete the original virtual machine after it's captured.
The latest version of PowerShell is 3.6.0, you can install it from this page.