What Mikal says it's my number one suspicion also,
I have the feeling that maybe C3 Picks the wrong IP to use when it detects more than one IP.
I have this issue also with the "Browsersync" that we use when I start the server it detects two IP addresses, one is the good one and the other one is the one that is reserved for the VM when it's in use but for me is not a problem because I open the URL with the correct one using the right IP manually I don't use the one that "Browsersync" gives me.
Example:
Browsersync shows me on the Command Prompt that my external IP is
187.134.1.4 so the URL is like this 187.134.1.4
But that is the wrong IP because it's for the VM, so I have to adjust it manually with my right IP like this 196.467.1.2
If c3 Remote Preview chooses automatically our IP that could be one of the problems.
It could be easily checked if this is the case if we had on C3 Settings the option to add our IP manually to be used for C3 Remote Preview as we do on C2.