Here's one that uses almost no storage, by seeking back to the last PATTERN1 and re-reading the input file. Note that this will not work on a pipe.

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11111545
use warnings;

my $fh = *DATA; # FIXME to your input file, DATA only used for testing

my $lastpattern1;
while( <$fh> )
  {
  if( /PATTERN1/ )
    {
    $lastpattern1 = tell($fh) - length $_;
    }
  elsif( $lastpattern1 and /PATTERN3/ )
    {
    seek $fh, $lastpattern1, 0;
    while( <$fh> )
      {
      my $end = s/ (?=PATTERN3)/\n\n/;
      print;
      $end and last;
      }
    $lastpattern1 = undef;
    }
  }

__DATA__
PATTERN1 SOME INFO

TEXT1

TEXT2

TEXT3 PATTERN2 SOME INFO

PATTERN1 SOME INFO

TEXT4

TEXT5

TEXT6 PATTERN3 SOME INFO

PATTERN1 SOME INFO

TEXT1

TEXT2

TEXT3 PATTERN4 SOME INFO

PATTERN1 SOME INFO

TEXT4

TEXT55

TEXT6 PATTERN3 SOME INFO
[download]

I also do the fix up on the PATTERN3 line, though I'm curious if that was just a typo on your part?