Download the ISO update package and mount it to the appliance to perform the upgrade instead.
I can definitely do that but I'm trying to avoid that since the product is supposed to be able to upgrade itself.
It's probably because the depot address is incorrect (a bug). This isn't the first time this has happened. Normally, yes, it can download the bits but in this case the address is wrong. Also, yes, vSphere Replication is a buggy and flaky product. Keep in mind it's free, though (included).
I dont think the Upgrade depot works anymore. AFAIK that feature was discarded. You will need to use ISO for upgrades now.
PS: 8.1 is going to be a migrate, not an in-place upgrade.