Overview
You experience that e-mails sent to your FogBugz Connected Mailboxes configured on your FogBugz On-Demand instance are not creating cases, only the main "cases" account is working with the address cases@yourfogbugzinstance.fogbugz.com.
Solution
Your firewall settings might be preventing our FogBugz Heartbeat Pinger service to connect to the email server hosting the mailboxes configured under Avatar Menu -> Mailboxes.
Verify that you have whitelisted in your firewall all the IP Addresses and Domain Names for FogBugz and Kiln On-Demand.