Intermittent unavailability of an instance in a failover cluster while a standby node is offline in a SQL Server 2008 failover cluster
Solution 1:
Have you got the log from the web server that was failing to get a SQL connection? There might be a clue in there.
This is a bit concerning though:
"The system detected that network adapter Local Area Connection* 9 was connected to the network, and has initiated normal operation."
"The system detected that network adapter Cluster was connected to the network, and has initiated normal operation."
Within 30 seconds of each other at the end of the outage.
What is Local Area Connection 9? I'm assuming "Cluster" is the heartbeat connection to the other node... so that would make this your domain connection? If so, given that we don't see an entry for it going down, it sounds like it was unplugged too during your maintenance...