Weird. I can reproduce OPs issue:

$ cat /tmp/x
my $regex = '(2[0-4]|1?[0-9])?[0-9]|25[0-5]';
while (<>) {
    chomp;
    if ($_ =~ /^$regex$/) {
        print "$_ matched\n";
    } else {
        print "$_ did not match\n";
    }
}
$ perl /tmp/x
100
100 matched
200
200 matched
300
300 matched
^C
[download]

In fact adding any "|<something>" seems to trigger it, i.e.

my $regex = '(2[0-4]|1?[0-9])?[0-9]|a';
[download]

gives the exact same result, and additionally matches anything starting with "a".

Aha. Looks like switching from

my $regex = '(2[0-4]|1?[0-9])?[0-9]|25[0-5]';
[download]

to

my $regex = qr/(2[0-4]|1?[0-9])?[0-9]|25[0-5]/;
[download]

seems to fix it. I don't immediately see why though.