Are the files completely empty, or is there a blank line? You're overwriting the combined log file, not appending to it, which may be part of the problem. You will also run into trouble if a line evaluates to false. I'd probably write:

open( my $fh, '>>', '/var/tmp/test.log' ) or die "Cannot open file: $!
+\n";
select $fh;
print while <STDIN>;
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That's untested, and it requires Perl 5.6.0 or better.