lammert - 3:20 am on Apr 28, 2011 (gmt 0)
Hi RonD, first of all Welcome to WebmasterWorld!
SSH has different authentication methods with username/password, certificates and keyboard interactive. It could be that the SSH client of server A is trying an authentication method which is not enabled on server B.
A second option could be the /etc/hosts.allow file on server B. There could be some rules affecting SSH requests from remote servers.