Ok, I have tried your solution, surferTim.
My code is now as before but with the part you specified replaced with your code.
Unfortunately, now I am not getting one successful post. Here is what comes up in the serial monitor on two separate attemps:
Wifly begin
Wifly join
connecting...
connected
Getting response
HTTP/1.1 200 OK
Date: Tue, 13 Mar 2012 19:31:23 GMT
Content-Ty
Wifly begin
Wifly join
connecting...
connected
Getting response
PUT /v2/feeds/51584.csv HTTP/1.1
ERR: ?-Cmd
<2.21>
Host: api
It seems now that the server doesn't close the connection and therefore it just hangs.
I'm really stuck at this point... again, any help would be great.