derby pointed out the problem with my approach. I think BrowserUK's idea of sliding buffers is probably best, but you can salvage my approach by opening three file-handles and having them in different frames. In code:

open(IN1, "<$infile");
open(IN2, "<$infile");
open(IN3, "<$infile");

my $temp;
$temp = <IN2>; # remove one dummy line from 2nd file-handle
$temp = <IN3>; 
$temp = <IN3>; # remove two dummy lien from 3rd file-handle

# Now process all three file-handles separately
# in chunks of three lines
[download]

And there was a recent node on how to read a file in chunks of n lines, that may help.