Your problem is that you're trying to read from DATA again for each line. But after the outer loop's first iteration, DATA is exhausted and won't return anything anymore, so the inner loop's body will not execute anymore.

You can reset the filehandle using seek to start reading from the beginning again - disclaimer, I've never tried that on DATA -, or (better) you could read from DATA into an array and iterate over that in your inner loop instead.

my @IPs = <DATA>;

foreach $confLine (<$in>) {
    if ($confLine =~ /ip4-address address=\"/) {
        foreach (@IPs) {
            my $ip = $_;
                if ($confLine =~ /ip4-address address=\"$ip/) {
                $confLine =~ s/\/>/update\"\/>/;
            }
        }
    }
    print $out $confLine;
}

___DATA___
1.2.3.4
1.2.3.5
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Also, just for general reference: you can stick labels in front of loops and pass a label to next to have it start the next iteration of a specific loop, e.g.:

INPUTLINE: foreach my $line (<<>>) {
    chomp $line;
    foreach my $pattern (@patterns) {
        $line =~ $pattern and do {
            say "$line matched $pattern!";
            next INPUTLINE;
        }
    }
}
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This also works for last and redo.