Mayday (as a distress call) has nothing to do with the first of May. It is the pronounciation of the French phrase "m'aider".

It originated in ~1923 and was adopted in 1927 by the International Radiotelegraph Convention of Washington (PDF warning) as the replacement for SOS. Page 80 of the PDF linked has the new rules for distress calls:

"The same rules apply to the radiotelephone distress call which consists of the spoken expression MAYDAY (corresponding to the French pronunciation of the expression " m'aider ")."