It might improve things a bit if you rearrange your if statements, you don't need to check ($A + $B == 2...) for each line of the input file, as you know that $B can only change when you've matched RTINSECONDS so you could do this instead :-

    if ($line =~ /TITLE=(.*)/) {
        $title=$1; 
    } 
    elsif
    ($line =~ /RTINSECONDS=(.*)/) { 
        $RT=$1;
        if ($title && grep {$_ eq $TI} @IDS) {
            $IDrtPairs{$TI}=$RT;
            $title = undef;
        }
    }
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As already mentioned it will be better to use a hash, so you should do that too :)

The example input data looks like TITLE & RTINSECONDS are always at the beginning of the line so you could anchor your regexs too, so it can reject non matching lines quicker. i.e. /^TITLE=(.*)/