The intermittent connectivity issue where some internal hosts can connect to an external public server while others receive an ICMP Host Unreachable message suggests a misconfiguration in the NAT Access Control List (ACL). The NAT ACL is responsible for specifying which internal hosts are allowed to translate their private IP addresses to public IP addresses. If the NAT ACL does not match all internal hosts, only some hosts will be able to establish a connection, leading to the observed intermittent connectivity.