However the loop never enters again in case of a wrong input.

Well, a while loop stops when the condition isn't true anymore. That's a feature ;-)

If you don't want that behaviour, don't use a while loop with the regex match in the condition, rather something like this:

while (<>) {
    chomp;
   if (m/your regex here/) {
        # work with it
   } else {
       print "Input '$_' not recognized as a date\n";
  }
}
[download]

Update: I think you shouldn't try to match only numbers in the allowed range, because it makes the regex overly complicated, and you won't catch all errors in the regex anyway (think of February 30th), so you have to validate your input after the regex in any case.

Something as simple as m/^\d\d-\d\d-\d\d$/ might do for you.