Your Internet drop means wire or wireless? And how many devices you connect to 8951? When the Internet drops, can you login in 8951's web page? And what's the status of the ADSL and Internet light?

Can you set static IP on your Laptop, and check whether it will have access to the Internet :)

Select the IP addresses which are permitted to access to the modem router remotely. With the default IP 0.0.0.0, any client would be allowed to remotely access the ADSL modem router

You can make such settings in Firewall-->LAN Host or WAN Host, if you don't know the detailed steps, you can refer to FAQ :)

What's the version of your MAC system?

I'm afraid there is no silimar setting on TD-W8968 :(