When i log onto RHP, i generally look at the little moves waiting bar at the top. This is an excellent idea as it means i can just glance at the website and see if i have any moves waiting or not. So if i don't have any, i don't waste my time looking.
However of late i keep having the same problem. If i'm making a number of moves in one game against an active opponent, i keep flicking back to the website, seeing the move waiting and then making it. But on occasion i get checkmated and don't realise it. So i keep looking back at the site and seeing my opponent hasn't moved and so leave, never realising the game has finished.
I think it would be useful to add another line saying "1 game finished" (as an example) alongside, that appears when neccisary, to stop this happening