By the attached logs I see you're running SQL Server 2005 on Windows Server 2003 (R2). Is it on old hardware too? Maybe that's the problem?

The system and application logs doesn't tell much. The communication errors seems to correlate with the cluster resource failing. Does the cluster have any logs you can look into?

Judging by the frequency you're experiencing  this problem my recommendation is to start migrating your database environment to newer versions of SQL Server and Windows Server instead.