Is the problem that it isn't upgrading modules that are already installed? Or that it isn't installing them at all?

If the problem is that it isn't upgrading the dependencies, you can do that with a command like cpanm --showdeps -q . | cpanm

If the problem is that it isn't installing the dependencies, it's really hard to say without more information. cpanm --showdeps . may help see what dependencies are being seen. But "stops soon without complains" doesn't give much to go on. cpanm's -v flag may help.