This fails because your lookbehind isn't anchored. You can either anchor it where you want or if it's really always at the start, replace the lookbehind with a lookahead like so:

while (<DATA>) {

    if (/^(?!TAGS)(.*?)(?=TAG2)/xgi ) {
        print "Negative lookahead: ";
        print $1, "\n";
    }
}
#
__DATA__
TAG1 text one TAG2
TAG1 text two TAG2
TAG1 text three  TAG2
TAGS text four   TAG2
TAG1 text five TAGT
TAG1 text six TAG2
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