I take it your modem is doing the ppp stuff, and is doing a- I think it is called dhcp passthrough - to send you your IP address.
These dhcp passthrough (I think it is also called many other things, so that will make searching difficult) setups in modem/routes are strange beasts, and work in several very poor ways. They do not use the protocols in any standard ways, and hence regularly cause problems.
Switching to using PPPoE might be an answer, but you will have some MTU issue;, or moving to a router that can run one of the open-source linux firmwares, that you can tweak to your heart's content.
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