I don't have a Mon Monogram wallet. I do, however, have a Pocket Organizer with a painted design on it, and some of the paint has chipped away. I stopped using it after a year and got another Pocket Organizer.
Unless there is a varnish applied on top of the entire item, the paint can and will chip away. The only way it won't happen is if you baby your item, which is probably the case for the people who say their Mon Monogram item hasn't had paint that has worn away.
Do not buy a Mon Monogram piece or any painted piece and expect that you can treat the item like normal and the paint won't chip or wear away or become scratched. If that is your expectation, then you will be sorely disappointed--especially with something like a wallet that easily and constantly brushes against pockets and other items while it's being carried. I mean, I suppose you could be ridiculous and put the wallet inside a plastic bag or felt sleeve and then put it into your purse. But, again, you would be ridiculous.