Ask this. How are you determining that the internet is dropped?
1) Your symptoms are exactly the same as a WiFi loss, without WiFi you have no access to the router.
2) The same applies if your laptop jumps over to another AP, another network. Not being on the same network you will not see the router. Has your IP address changed?
3) (finally) I would hope you are using a private address for this, not the internet (or WAN) address.
4) Typically not only should you be able to access the router, but also the modem (upstream network). Even if the modem cannot connect.
e.g. laptop 192.168.0.120 --> router 192.168.0.1 -/-> modem 192.168.100.1
These are example class C ip addresses.
After three years I am posting this answer for the "searchers".