I did perl -le 'print for <*>' | wc -l, and it listed out over 100000 files (after a while). I don't think the size of your directory is the problem. It still could be the problem if your memory is very limited, but I'd expect you to get a message about that explicitly if that were the case. (The file globbing you do builds up a list of all those 60000+ files in memory at once.)

The problem may be that after mkdir, you or into a string. The string doesn't do anything. You may want:

mkdir "$dst2\\$datestamp2"
    or die "Can't mkdir '$dst2\\$datestamp2': $!\n";
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After that, I expect the move to fail too, but the warn there should be telling you why. If it's not, I wonder if STDERR is being redirected, or there's a $SIG{__WARN__} handler or something.

I'd make your end-on-limit more explosive:

if ( $count > $limit ) {
    die "limit exceeded: $count files processed";
}
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Generally I recommend setting $limit to about 10 and sprinkle a lot of print statements in the loop to make sure all those variables have the values you think they do.