That's very odd.
Algorithm-Permute-0.12 builds fine for me on Cygwin, and the command that fails for you is exactly the same as the command that succeeds for me.
If the approach suggested by roboticus doesn't yied anything, check the permissions of coollex.c. (For me, they're -rw-r--r--)

I often have trouble building modules for Cygwin if the build directory is outside of the Cygwin tree, but it looks to me that your build directory is probably inside the Cygwin tree anyway.

Cheers,
Rob