OK, I have made change as you mentioned. Tested it, the error is still same as before (Error 404 - File or directory not found).
here is the log:
Jul 9 16:39:32 tmm tmm[1577]: Rule ProxyPass : beta, Host=www.site1.com, URI=/support/: Looking for entries matching www.site1.com/support/
Jul 9 16:39:32 tmm tmm[1577]: Rule ProxyPass : beta, Host=www.site1.com, URI=/support/: Found Rule, Client Host=www.site1.com, Client Path=/support, Server Host=www.site2.com, Server Path=/support
Jul 9 16:39:32 tmm tmm[1577]: Rule ProxyPass : beta, Host=www.site1.com, URI=/support/: New Host=www.site2.com, New Path=/support/
Jul 9 16:39:32 tmm tmm[1577]: Rule ProxyPass : beta, Host=www.site1.com, URI=/support/: Using default pool betapool
Jul 9 16:39:32 tmm tmm[1577]: Rule ProxyPass : beta, Host=www.site1.com, URI=/support/: Removed Accept-Encoding header
Jul 9 16:39:32 tmm tmm[1577]: Rule ProxyPass : beta, Host=www.site1.com, URI=/support/: $stream_expression_cmd: STREAM::expression "@www.site2.com/support@www.site1.com/support@", $stream_enable_cmd: STREAM::enable
Jul 9 16:39:32 tmm tmm[1577]: Rule ProxyPass : beta, Host=www.site1.com, URI=/support/: Successfully configured and enabled stream filter
Thank you very much,
Victor