The current spelling of 'heyday' arose as a folk etymology. In the early 1500s (first recorded in the 1520s), it was heyda, and was used akin to hei or hurrah, a happy exclamation of playfulness or surprise.
By 1751 it was being used in its current sense, to mean the period of time in which one was most successful. At this time it also picked up its new spelling, presumably simply because it felt like a more sensible word if it was composed of more familiar parts. However, the spirit of the word might best have been served if they had spelt it hurrah-day.