In a nutshell:

• Boxes are never accepted on southbound nonstop/direct AA-operated flights to Port-au Prince, Recife, and Salvador.
• During the summer and winter months, boxes are not accepted on southbound nonstop/direct AA-operated flights to these cities. Exact dates vary but the summer embargo is generally June-September and the winter embargo is generally November-January. Seasonal embargoes are generally posted at least one month in advance. Some exceptions may apply for sports items, strollers (to Brazil only), and military personnel.
• AA's definition of a box includes plastic tubs, containers, and coolers.

Boxes are otherwise accepted without issue on all other flights but are subject to the standard baggage weight and size restrictions.