[CentOS] Basic KVM networking question

A CentOS 6.3 box ("host") runs several KVM virtual machines, each of which 
has two interfaces attached to the two bridges br1 and br2 (and each thus 
has two IP's; one on 192.168.0.0/22 and one on 192.168.4.0/22); 
net.ipv4.ip_forward on the host is 1. Simplified diagram:

                                host
                          +---------------+
                          |               |
   net1 = 192.168.0.0/22  |               |          net2 = 192.168.4.0/22
   -----------------------+  br1      br2 +---------------------------------
           |              |               |                |
           |              |               |                |
       Client A           +---------------+            Client B
                        (hosts KVM1, KVM2, etc)

Each client uses the bridge's IP address on the same side as default 
gateway. Client A can successfully ping or ssh (for example) to a KVM 
machine by IP address by using the KVM machine's net1 IP address. Client B 
can likewise communicate using the KVM machine's net2 IP address. However, 
neither client can communicate by using the address on the opposing 
segment (eg, Client A using KVM1_net2_IP); I can see from tcpdump that the 
packets are received by the virtual machine but no reply is ever made. Any 
clue?

Steve