Why does an air-conditioner need maintenance and a fridge does not

A refrigerator is different from a (whole house) A/C in a few ways.

• Similar to a window unit A/C it's a "factory built packaged unit" - it's been assembled and tested under carefully controlled conditions on an assembly line. In my experience, other than cleaning the filters, a window A/C does not need "regular service" and like many refrigerators when it does hit a point of needing service it's not designed to be easily serviceable, and it is usually non-economical to repair the refrigeration system when it does fail, eventually.
• A refrigerator is normally running several to many times a day, every day, every month, every year.
• A whole house A/C is field assembled from components. The joints that are assembled in the field are often mechanical, though they are sometimes brazed, but they are brazed under field conditions which are often not ideal, while a factory-made unit will be brazed under nearly ideal conditions. The lines run long distances exposed to potential damage. There is far more potential for leaks.
• Any A/C is usually not running many months of the year, and sometimes this causes problems with components that have sat idle for months when the system starts up again. Corrosion or decay may be more likely.
• Most A/C units have parts that sit out in the weather. Most refrigerators do not.

A refrigerator should be cleaned regularly, especially the airflow around the coils, which is maintenance. I assume from your question wording that you are referring to active maintenance of the refrigeration system contents, not cleaning (which is maintenance and does prolong its life.)