How long are the lines in the file? Unless they are extremely long what you have shown should be fine. Are you sure you are not leaking memory in the loop or accumulating data in the loop? As a sanity check you might like to try:

open my $fh,...
while (<$fh>) {
}
close $fh;
[download]

and check that that runs correctly. Assuming it does, start adding back the contents of the while loop and see where the problem happens. If it doesn't run correctly (terminate cleanly) you need to rethink what constitutes a line and possibly come back for more advice.