Bear in mind that the current through the low voltage cable will be proportionately higher than the mains lead. Assuming the router takes 12V, the current will be 20 times that of the 240V mains supply.
The problem then is that voltage drop along the cable, being proportional to current, will also be 20 times as much, and may become significant enough to cause a problem. Note my emphasis on 'may', I'd not like to speculate on how long the extension would actually have to be to cause any symptoms... it all depends on a actual current draw, cable thickness, and voltage operating range.