If I didn't know better, I'd say ssh is detecting the lack of a terminal and assuming it's in batch mode. I thought Net::SSH was native perl, but now I wonder if it has forked a /bin/ssh? ssh will definitely drop into "batch mode" from chron unless it's told not to do so, and afaik it won't accept passwords when it considers itself to be non-interactive.

Perhaps you should set up a keypair?

Update: duh. The native perl ssh has a different name: Net::SSH::Perl