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>'