I just came across this post, I too have a cybot and easily copy files from win 7 64. The way to do it is :-
1, click on start, right click computer, click manage, this opens computer management.
2, left click device manager, and with the cybot remote connected, check that the hand set is set to either com 1 or com 2,
3,right click on whichever port it is on and open properties - port settings and set baud rate to 9600.
4, open the advanced tab (if it on some other port like 56, change it to port 1 or 2, you will probably get a msg that its in use but don't worry about that at the moment )
5, this is the important bit! uncheck the "use FIFO buffers......." box, then move the sliders for rx-tx buffers to MINIMUM!
6, click ok, then ok again.
7, go to programs, R click on the cybot cd you want files from, click expand, open the cybot program you want, follow the instructions in the cybot dialogue box (check the correct port) and it should download correctly.
8, once you have finished, open the device manager again and re-set the port to default.
I hope this helps, it took me a while to figure it out but everything seems to be working fine 
P.S I use a cheap Maplins USB to RS232 adaptor to connect to the computer.
PPS. If you still have problems, you may have to lower the baud rate to 4800.