How can maintain my permanent resident alien if I want to reside in Mexico my domestic partner of 12 years and still work in U.S.?

As a legal resident alien, you can file Form I-131 Re-entry which will allow you to remain outside US for 2 years. This is a temporary band aid and in the end, you and your partner should consult with an experienced immigration attorney who can devise a more permanent solution one that hopefully can bring your partner back to the US on a full time basis.

There is a special green card for commuter. This way, you can work in San Diego and return home to TJ every night. A form needs to be filed to reflect your commuting status. You need to be currently employed and must provide a letter from your employer. Time as a commuter doesn't count as residence for purpose of applying for naturalization. Another potential option would be to naturalize. You must have your green card for 5 years, speak, write English, and have good moral character. There are other requirements as well, so it is best to consult with an attorney to make sure you qualify. Many attorneys have free initial consultation.