When you move to Mexico or other foreign countries you MUST notify the IRS of your new address. The IRS is not responsible to keeping its records up to date with your new address, you are! You should notify them using Form 8822. If you fail to notify them of the address change, any notices they send to your previous address are deemed received under the law, and various time limitations, assessments, etc. , may expire even though you are not receiving the IRS notices.
One client who failed to notify the IRS of her new address was erroneously assessed a large sum of money and only learned about it many years later when the IRS took levied and took all of the money out of her bank account. It was very expensive and time consuming to finally convince the IRS of their error and get her money refunded. The problem would have never happened if a Form 8822 had been filed. The error could have been corrected immediately when the initial erroneous assessment was made.
Due to poor mail delivery in many countries, it is wise in some situations to keep using a US mailing address of a friend or relative, so your IRS notices will be delivered to a competent person who can then forward the mail by fax, email or a private delivery service.