Core issue
This problem occurs due to the presence of the Cisco bug ID CSCei23290.
Resolution
In order to resolve this issue, remove the static command that matches the inside interface IP (the source of the Dynamic Host Control Protocol [DHCP] requests). For translations, use Port Address Translation (PAT) or Network Address Translation (NAT) instead of the static command.
An upgrade to PIX version 7.1.x also fixes this issue.