When updating MinGW, and selecting mingw32-make for install, I noticed the tarball was being deleted from the installation directory. Other tarballs (like g++) were kept.
As I found out, after unpacking, the installer tries to clean up by removing files named mingw*.* from the installation directory. Sadly, the mingw32-make tarball fits that description...
A solution is to restrict the deletion to files named mingw*.ini and mingw*.exe .