Info I put in this post about using PowerShell 3 to connect to ESXi via CIM might help. Could see if you're not able to connect via this method when the proble arises. If so, a script could be written to check periodically and alert when connections fail: http://communities.vmware.com/message/2195127
But have you checked the logs to see if there's any info on why CIM server is having problems?