Response.Close sends a reset packet to the client and using it in anything other than error condition will lead to all sorts of problems - eg, if you are talking to a client with enough latency, the reset packet can cause any other response data buffered on the server, client or somewhere in between to be dropped.
In this particular case, compression involves looking for common patterns within the response and some amount of response has to be buffered by the compression code to increase the chance of finding longer repeating patterns - this part that is buffered cannot be sent to the client once you do Response.Close().
In short, do not use Response.Close().