Had a developer who worked for me who did something very similar. Lived all over the world, would get short term visas, and return to Mexico if needed to await his next visa. He had a friend that let him use his mailing address for work and mail and slept on his couch or in hostels while awaiting a new visa. He loved the life. Lived on a dozen different beaches while he was working for me. Apparently a Mexican visa is one of the easiest to get.