An approach reading a line at a time rather than slurping the whole file.

use strict;
use warnings;

open my $inFH, q{<}, \ <<__EOD__ or die $!;
Title 1
Line of text A
Line of text B
Title 2
Line of text C
Title 3
Title 4
Line of text D
__EOD__

my @groups;
while ( <$inFH> )
{
    if ( m{^Title} )
    {
        unshift @groups, [ $_ ];
    }
    else
    {
        push @{ $groups[ 0 ] }, $_;
    }
}

while ( my $group = shift @groups )
{
    print @{ $group };
}
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The output.

Title 4
Line of text D
Title 3
Title 2
Line of text C
Title 1
Line of text A
Line of text B
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I hope this is of interest.