This is truly a perplexing problem. Here's a possible solution involving pipes: (tested code)

#!/usr/bin/perl
use strict;
use IO::Handle;
pipe(READ,WRITE) or die;
READ->autoflush(1); #just to be safe
WRITE->autoflush(1);
my $data=<DATA>;
print $data;
print WRITE $data;
*DATA=*READ;
my $data2=<DATA>;
print $data2;
__DATA__
TESTDATA
[download]

It kind of shocked me that *DATA was not read-only. After reading from the pipe, just write the same thing back and you'll have an infinite supply of DATA. This can be easily adapted for lines of DATA but be beware of autoflushing. I came across some pitfalls involving non-flushing data in the handles when I was doing something similar.

AgentM Systems nor Nasca Enterprises nor Bone::Easy nor Macperl is responsible for the comments made by AgentM. Remember, you can build any logical system with NOR.