Router (D-Link 624+) issue?

Ever since I moved to a new apartment I’ve been using a D-Link 624+ router to connect to the internet (via DSL). The comp’s hooked up through LAN - not WLAN. Strangely enough, whenever I’m not accessing the internet for a while, e.g. working on something or playing a game, and then start surfing the web again some websites refuse to load. Some sites will load, but others like Gmail cannot be found. Doesn’t go beyond the “looking up” process just to note that they cannot be found seconds later. It’s always the same problem and it’s always the same set of sites. I usually reboot to ‘solve’ the problem then.

The problem seems to occur no matter if the router’s set to connect on demand or to be always connected. I’m assuming it must be related to the router since I didn’t encounter the problem at my old location, where the computer was hooked up to a DSL modem directly. Any hints? Thanks.