Are you seeing entries similar to the following in your logs?

mDNSResponder Error -65537 for deregistration of service host\.example\.com._nssocketport._tcp.yourname.members.mac.com. 
mDNSResponder Update blue._ssh._tcp.yourname.members.mac.com. failed with rcode 2 
mDNSResponder ERROR: mDNSPlatformReadTCP - SSLRead: -9806 
mDNSResponder ERROR: tcpCallback - attempt to read message length failed (-1) 
mDNSResponder ERROR: socket closed prematurely tcpInfo->nread = 0 
mDNSResponder KQ SSLHandshake failed: -9844
mDNSResponder KQ SSLHandshake failed: -9806 

Well, it might be that the issue lies with Apple’s “Back to my Mac” service.

Please carefully examine the following file: /Library/Preferences/SystemConfiguration/preferences.plist, in particular, look at the dictionary for key BackToMyMac:

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        <key>System</key>
        <dict>
                <key>Network</key>
                <dict>
                        <key>BackToMyMac</key>
                        <dict>
                                <key>502</key>
                                <string>yourname.members.mac.com</string>
                        </dict>
                        <key>HostNames</key>
                        <dict>
...

There should be one numeric key with your user id (502 in the above example) and a string with the fully-qualified hostname <yourname>.members.mac.com`.

If this is not the case, sign out of Mobile Me, remove the BackToMyMac key and its dictionary and sign in again.

Typical issues that lead to problems are: 1. changed user id 2. removed user that was signed in to Mobile Me 3. used Migration Assistant