Hopefully the router is Wireless N. If the router is Wireless N, then range and speed should not be a problem.
As well, unlike the iPhone, I notice that if you hold the iPod Touch in certain positions, the WiFi Signal is subject to degrade in bars. Then again, try holding the iPod Touch the way you usually do near the room where the router is. IF the signal still degrades, then the theory works.
IF not, then the iPod Touch is obviously passing through thick walls to get the WiFi signal in the ground floor from the second floor.