After a little tidying to turn the code into a stand alone sample I don't see the problem you describe given the data you've supplied. Consider:

use strict;
use warnings;

my $match =
    'ArAuthFrameworkImpl::doPostAuth.*Authentication\s*mechanism\s*ret
+urned\s*\[(..*­)\]\s*for\s*AuthIdentity\s*\[(..*)\]';
my $outText;

open my $outFile, '>', \$outText;

while (my $line = <DATA>) {
    chomp ($line);
    if ($line =~ /^(.*)INFO:.*QNA Step - AUTH IN PROGRESS/) {
        my $Time_Stamp = $1;
        printf $outFile "$Time_Stamp,";
        QnA_search_for_sucess_or_failure ();
    }
}

close $outFile;
print "\n\n$outText\n";


sub QnA_search_for_sucess_or_failure {
    while (my $line = <DATA>) {
        if ($line =~ /QNA Auth.*Success\s*and\s*Complete/) {
            printf $outFile "Success,";
            print "In Success,\n";

            my $ErrorMsg = "null";

            while ($line = <DATA>) {
                if ($line =~ /$match/) {
                    print "$2\n";
                    printf $outFile "$2, ${1}, $ErrorMsg\n";
                    return;
                }
            }
        }

        if (defined $line
            and $line =~ /Message.*QNA\s*Auth\s*Failed\((..*)\).*/)
        {
            my $ErrorMsg = $1;

            printf $outFile "Failure,";
            print STDOUT "In Failure,\n";
            while ($line = <DATA>) {
                if ($line =~ /$match/) {
                    print "$2\n";
                    printf $outFile "$2, ${1}, $ErrorMsg\n";
                    return;
                }
            }
        }
    }
}

__DATA__
Tue May 19 22:55:13.649 2009 Morocco Standard Time INFO:    pid 2172 t
+id 3412: 160: 10083504: QNA Step - AUTH IN PROGRESS
Tue May 19 22:55:13.649 2009 Morocco Standard Time INFO:    pid 2172 t
+id 3412: 160: 10083504: QNA Auth - Success and Complete, Returning SU
+CCESS
Tue May 19 22:55:13.665 2009 Morocco Standard Time INFO:    pid 2172 t
+id 3412: 17: 10083504: ArAuthFrameworkImpl::doPostAuth::1:10083487:: 
+Authentication mechanism returned [0] for AuthIdentity [12345]


and for QnA failure the line comes like this in place of success line-
+-
Tue May 19 22:56:21.962 2009 Morocco Standard Time INFO:    pid 2172 t
+id 688: 160: 10083554: Err[115261735], Message: QNA Auth Failed(Inval
+id Credentials), Repeating the challenge and Returning FAILED
[download]

Prints:

In Success,


Tue May 19 22:55:13.649 2009 Morocco Standard Time ,Success,
[download]