You could try this:

#! perl -slw
use strict;

my $para = do{ local $/; <DATA> };
$para =~ tr[ \t\n][ ]s; ## normalise whitespace

my $longest = '';
length( $1 ) > length( $longest )
    and print '?', $longest = $1
    while $para =~ m[(.+)(?=.*?\1)]ig;

print $longest;

__DATA__
Ah, I am kind of embarrassed not to have thought of this.
I was so focused on look ahead, for some reason, but yeah,
this works. The thing is, I need to match more than one
sentence, potentially whole sections of texts can be
duplicated and I need to find them. I will try your solution
see how it goes. Thanks!I am kind of embarrassed not to have
thought of this for some reason, but yeah, this works. The
thing is, I need to match more than one sentence,
[download]

Outputs:

C:\test>junk24
?Ah,
?I am kind of embarrassed not to have thought of this
?for some reason, but yeah, this works. The thing is, I need to match 
+more than one sentence,
for some reason, but yeah, this works. The thing is, I need to match m
+ore than one sentence,
[download]

Remove the print '?', once your happy it is doing the right thing.