I want to suggest another solution https://github.com/nerd220/JSONext

It allows you to easily serialize objects, saving internal and external links, methods and prototypes.

In subject case:

var p1 = new Person(77);
var serialize=toLinkedJSON(p1,[],['Person']);
var p2 = fromLinkedJSON(serialize);

p2.isOld(); // true, now this method is works