The reason is the "g" (global) option. The "g" option means that the next search will start where the last search succeeded. There is a counter associated with the string being searched that can be accessed using the "pos" function. The search starts from "pos($regexp)". See a modified version of your code:

#!/usr/local/bin/perl
use strict;
use warnings;

my $regexp = 'Perl Monks';

if($regexp =~ m/^Perl Monks/gi) {
    print "\nFound..";
} else {
    print "\nNot Found..";
}
print "\npos = ".pos($regexp)."\n";

if($regexp =~ m/^Perl Monks/gi) {
    print "\nFound.1.";
} else {
    print "\nNot Found.1.";
}
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when you run the code you obtain:

$ perl /tmp/prueba.pl

Found..
pos = 10
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Since "pos" is now 10 the regexp will not match from that position.
Try to eliminate the "g" option the second time and the regexp will succeed.