How about the LED lights status when it disconnected? If DSL light is flashing or off, try this http://www.tp-link.com/en/faq-735.html
If the DSL light is on solid at that time, login to D9's web UI to check its DSL line status and WAN status. If there is still a WAN IP address? If the DSL line status/quality is acceptable? http://www.tp-link.com/en/faq-546.html

Had internet for 3 years here
Never any problems
Only with this modem. Now today NO WIFI
Internet over cable lan works
Adsl led light is on and also wifi led lights are on
But NOT internet led
Have done a reset and basic setup and also called my internet provider in Italy (infostrada) twice.

I think you can check the firmware and hardware version and look for a update.

Thank you for your reply @vieldcs
I had already updated the firmware I'll paste here the version that I have now
firmware: 0.9.1 0.1 v0041.0 Build 150826 Rel.42046n
hardware: Archer D9 v1 00000000
I had disconnected the modem for a couple of days and reattached my old one as wifi was not working.
Today connected the TP-Link Archer 9 modem to try to figure out what the problem was and everything is working as a charm without me doing anything .. go figure!
Hope this state of bliss it lasts a little longer than last time !

Here I am a year later with the same problem. (a bit of a nightmare)

My modem supplied by my isp doesn't disconnect as the tp-link modem does but unfortunately has a limited wi-fi range

I set factory defaults and updated firmware. I am clueless on other possible remedies

Thanks in advance

M.