FWIW, I've been playing these games from my laptop on a wireless connection, and haven't experience any problems with getting through the multiple rounds of the game.
Whilst playing "Countdown" last night, however, I did run into a lone problem when the network dropped..the game kept going (i had just finished the last numbers round), but it lost connection with the database, I believe. When the conundrum came up, it showed as "AAAAAAAAA". When I rang in, the letters "NUERIFDNE" came up..spelling "UNDEFINED". I admit, as frustrated as I was with the game crapping out at the end, it did make me laugh.
Random observation: "Countdown" makes me feel dumber than a 5th grader. "Well, this number puzzle wasn't too hard..." has been followed by some choice words of my own in the last 24 hours. Still, I'm hooked.