'tinternet problem ?

[rikrobson]

Would those be possible reasons for only some sites causing the disconnection though ?
Most sites are fine.

The site cannot affect the connection. This is just coincidence and you are noticing the disconnect when accessing certain sites.

the router "syncs" with the equipment in the exchange over the line and this will not care what the traffic is. The traffic to and from websites is sent in packets. it could be some sites are more traffic heavy than others and because the line is slow you notice it more.

if it can be proved to be the site then the router is the problem, but it sounds like the line.