I am a US citizen living in Mexico. My passport will expire before I get back to the US. Must I make arrangements to return to the US to renew or do I have an extension on this?
This US State Department webpage says to renew your passport you must apply in person at the nearest US consulate or embassy in Mexico. There is no mention of "extension." The page's text is:
Apply Outside the United States
If you live in any other country besides Canada, you must apply in person at a U.S. embassy or consulate for all passport services. Each U.S. embassy and consulate has different procedures for submitting and processing your final documents, but the forms, supporting documentation, fees, and finished products are similar.
A US citizen is not required to maintain a valid US passport (although it might be a good idea to maintain one just in case). So, if you want, you could let it expire and only apply for a US passport at a US consulate the next time you need one (e.g. to travel to the US), even if that is many years after your previous US passport expired.