Yes, wired. It's a wired Ethernet-over-Power Line connection, see www.devolo.com for technical details. WiFi is turned off. Anyway, wired and WiFi use the same static IP address within the LAN, it's alway 10.0.1.2, the standard host for NAT port forwarding. The network setup has always been this way and never caused problems. It has been running smoothly for almost 18 months now, using LogMeIn, Plex, jDownloader, EyeTV and other stuff for remote access via iPhone, iPad or web interfaces. Glitches started after upgrading to ML.
I just had the idea that the DHCP lease time configured in the Time Capsule might be the source of the problem. It was set to three hours, which explains why the Mac mini (10.0.1.2) eventually disappears from the list of network devices after it went to sleep: IIRC the Bonjour Sleep Proxy discards the IP reservation as soon as the lease time has elapsed, making the corresponding network device unreachable. Well, I cannot remember I changed anything in the network setting of the Time Capsule, but increased DHCP lease time to 60 days now. As soon as I get home, I will push the Mac mini's power button to re-register it's IP in the LAN and check if the new DHCP lease time solves the Wake-on-LAN issue.
I wonder why I did not run into that problem with Snow Leopard or Lion. Maybe they really changed something under the hood with regards to the Power Nap feature. For now, it's just guessing, so any further ideas are warmly welcome.