Hi Anthony
When you said lose connection to the DHCP, what actually are meaning as in error you are seeing?
Note that phones will retain it's dynamic IP address even in the case of a temporary disconnection to the DHCP server, as long as the Mitel system is reachable.
The only time it will lose connectivity to DHCP is when the lease expires and it trues to get a new IP but could not reach the DHCP server.
In such case you will get a DHCP Discovery message on the set.
I would check the DHCP lease timer and see if this corresponds with the issue, and if it does check if you have the numbers of IP addresses to go around.
I have seen before that some DHCP server renews IP but does not release the pooland in which case there's not enough IP addresses to re-distribute.
Also what device is supplying the DHCP to the phones? Is it the MXe or a local DHCP server?
If it is the MXe, then I would say you check your DHCP settings and check for the above.
In terms of capturing logs, the 69xx phones can do DHCP trace.
Clever men learns what Wise men shares!