I waffled on some time ago about using proper certificates in your vSphere 5.5 environment. You can read about some of how to do that here. Eric has a nice summary of the steps here. I got a call recently from the customer about a few things and they mentioned some issues with vSphere Replication 5.8. Turns out I’d forgotten about vSphere Replication when I’d gone through the certificate replacement process, as it was done as a PoC. The fix is simple: power off the appliance and power it on again. VMware has a KB for most every situation, including this one – VMware vSphere Replication appliance no longer able to communicate with the VMware vCenter Server after changing the vCenter certificates (2063955). It also helps that I’m a bit late to this particular party.
The next step should be to replace the certificates on your vSphere Replication infrastructure as well. I was going to put together a post on that too, but it’s probably simplest if you read the VMware KB – Configuring CA Signed Certificates for VMware vSphere Replication (2080395). Friedrich also has a great post on some of the basics – including the certificate replacement process – here.