Here's a quote from Huber regarding lack of fertility after 20 days:
"It is undoubted, therefore, that when the copulation of queens is retarded beyond the twentieth day, only an imperfect impregnation is operated: instead of laying the eggs of workers and males equally, they will lay none but those of males."
And here is another quote from Huber about successful mating on the 16th day following emergence:
"On the sixteenth day, I set her at liberty: she left the hive, rose aloft in the air, and soon returned with full evidence of impregnation. In two days, she laid, first the eggs of workers, and afterwards as many as the most, fertile queens"