It’s a well-known path problem on your server: https://4684068.no-ip.org:1177/.well-known/caldav redirects to https://4684068.no-ip.org/remote.php/carddav/ (without port). So DAVdroid tries to connect to https://4684068.no-ip.org/remote.php/carddav/ (without port) and fails with “EHOSTUNREACH” which it shows to you.
$ curl -kvX PROPFIND https://4684068.no-ip.org:1177/.well-known/carddav/
* Adding handle: conn: 0xc48a20
* Adding handle: send: 0
* Adding handle: recv: 0
* Curl_addHandleToPipeline: length: 1
* - Conn 0 (0xc48a20) send_pipe: 1, recv_pipe: 0
* About to connect() to 4684068.no-ip.org port 1177 (#0)
* Trying 95.248.109.127...
* Connected to 4684068.no-ip.org (95.248.109.127) port 1177 (#0)
* Initializing NSS with certpath: sql:/etc/pki/nssdb
* skipping SSL peer certificate verification
* SSL connection using TLS_DHE_RSA_WITH_AES_128_CBC_SHA
* Server certificate:
* subject: E=me@my.org,CN=4684068.no-ip.org,OU=Bo,O=Dafuq Ltd,L=Caudum,ST=Slol,C=AT
* start date: Nov 02 14:42:26 2014 GMT
* expire date: Nov 01 14:42:26 2016 GMT
* common name: 4684068.no-ip.org
* issuer: E=me@my.org,CN=4684068.no-ip.org,OU=Bo,O=Dafuq Ltd,L=Caudum,ST=Slol,C=AT
> PROPFIND /.well-known/carddav/ HTTP/1.1
> User-Agent: curl/7.32.0
> Host: 4684068.no-ip.org:1177
> Accept: */*
>
< HTTP/1.1 302 Moved Temporarily
* Server nginx/1.2.1 is not blacklisted
< Server: nginx/1.2.1
< Date: Sun, 02 Nov 2014 17:07:02 GMT
< Content-Type: text/html
< Content-Length: 160
< Location: https://4684068.no-ip.org/remote.php/carddav/
< Connection: keep-alive
<
<html>
<head><title>302 Found</title></head>
<body bgcolor="white">
<center><h1>302 Found</h1></center>
<hr><center>nginx/1.2.1</center>
</body>
</html>
* Connection #0 to host 4684068.no-ip.org left intact