In the regex, changing \d*+ to \d++ fixes it, although I have to admit I don't see why yet, it'll take a bit more staring at it to figure that out... Anyway: WebPerl Regex Tester Link

Personally, I'd use Regexp::Common for this kind of task:

use warnings;
use strict;
use Regexp::Common 2013030901 qw/balanced/;

my $re = qr/$RE{balanced}{-parens=>'<>'}/;
print $re, "\n";

my @cases = ( "<1>" ,"<1,2>" ,"<1,2,<3,4>,5,6>" );
for my $case (@cases) {
    print $case, " ",
        $case =~ $re ? "matches: '$1'\n" : "doesn't match\n";
}

__END__

(?^:((?:\<(?:(?>[^\<\>]+)|(?-1))*\>)))
<1> matches: '<1>'
<1,2> matches: '<1,2>'
<1,2,<3,4>,5,6> matches: '<1,2,<3,4>,5,6>'
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