Getting rid of it won't help anything ... it's not like the Automatic Private Address is hijacking your stack. Apparently, your lease is expiring and isn't being renewed, or something similar.
You may want to check the advanced hardware options for you NIC. It's likely that the box is checked for "Allow Windows to put this interface to sleep to save power," and when the lease comes due, the NIC is asleep (or not "waking up" fast enough.
If the DHCP address is coming from a device you control, check the lease time, and maybe lengthen it some.
Good Luck
Scott