I tried to replicate the behavior you reported with a couple simple one-liners, and a url that seemed similar enough in nature to your made-up example:

perl -MLWP::Simple -e 'getstore("http://www.perlmonks.org/index.pl?nod
+e_id=640887","test1.html")'

perl -MLWP::Simple -e '($u,$f)=("http://www.perlmonks.org/index.pl?nod
+e_id=640887","test2.html"); getstore($u,$f)'
[download]

But I got the full page each time -- no problem. If you try it that way and also get full data each time (no problem), then I would expect there to be some other, seemingly unrelated difference between your two earlier script versions.

(I can't imagine what sort of server-side problem could be involved, except some bizarre coincidence.)