|I have to think your diagnosis is not correct.|
When you say router gets a new ip address that refers to its wan port. Your expander has no knowledge of its wan port so this does not apply.
Your expander only knows about the routers wifi lan.
"The router seems to lose connection frequently"
How frequently? Most dhcp scopes are in days not hours though a hotel maybe.
Is the expander getting a ip address?
Is it a dhcp address?
Answers are only as good as the information you provide.
How to properly post a question:
Sorry no tech support via PM's