A professional apology letter is one that attempts and successfully manages to carry through emotional content and still keep the message sounding professional by the choice of words used. The only way to maintain professionalism in any apology letter is to portray the situation as it is, explaining how the matters came to be and the position that one company takes as the one at fault to make amends. This may sound tricky blending remorse and business acumen in a letter that is meant to restore or maintain already shattered confidence in its dealings.
The few people who manage to do this are able to balance the emotional with the factual and are able to elicit the necessary response from the recipient of the letter and also leave room for future communication. The ability to clarify any muddled issues and take the blame for them while asking for pardon for the event gets to make the mistake forgivable and impresses on the recipient to accept and bury the hatchet for the sake of future business endeavors between the two parties. Those qualities alone qualify as a recipe of a professional apology letter.