The OBi110 does have a relay that connects the LINE Port directly to the PHONE Port as a fail-safe when no power is applied to the OBi. During reboots, this relay does cycle, making the clicking noise you hear. Since an OBi100 doesn't have a LINE Port, it doesn't have a relay.
The OBi shouldn't be rebooting when a DHCP lease is renewed. The OBi does reboot when an Ethernet connection is lost and restored.
Is your OBi updated to the latest firmware? There were some problems with DHCP in earlier versions.