My bitcoin-qt client connection status and uptime at http://blockchain.info/connected-nodes does not show reliably - why?
The list on http://blockchain.info/connected-nodes is just a list of nodes currently connected to that specific business' bitcoind server. It has no connection to the list of all Bitcoin nodes connected to other nodes. This hypothetical list doesn't exist anywhere, for obvious reasons, and would be 10 to 20 times longer than blockchain.info's list.

Blockchain.info's server is not authoratative in any way and has no formal connection to the "official" Bitcoin client (bitcoin-qt), the Bitcoin project, or Bitcoin.org.

As for the 360 minutes thing, Blockchain.info's bitcoind server probably prunes clients connected for 6 hours for whatever reasons that business has decided to do that. Or perhaps their bitcoind server lost its internet connection momentarily around 6 hours before you checked their connected nodes list.