It's probably a sort of warning against the other popular Mayday saying - Hooray, hooray, the first of May, Outdoor sex begins today.

This would give the risk of a child being born in February, a lean time of year when there was often not enough food, and the new crops hadn't reached an edible state yet. There would be a greater risk of the baby dying of cold and hunger, so it's a warning to keep your clouts on until June when a baby conceived would be born in March/April, thus having a better chance of survival.

LTS