Demons Lullaby Event
The Event runs from SS May 7th till SS May 14th, so you don't actually 'fail' until you fail to complete 6 tasks and and return the pleased baby to its Demon Mother when SS May 14th occurs, and your World server doesn't fail until 500 pleased Demon Babies are not returned to the Demon Mother at SS May 14th.
Once you click on the crying demon baby , the task is 'active' until the Event ends
The 20 hours you mentioned refers to the cooldown period between completing one task and starting another. This means you complete one task, the baby sleeps for 20 hours and after the 20 hours the baby starts crying and you can click on it and start the next task. Whether you click on it right after the 20 hours is up or any time after that doesn't matter. What matters is that the 6 tasks are finished and the 'pleased' Demon infant is returned to the Demon Mother before SS on May 14th
Edit for clarity on question asked in comments
Hope this answers your question, if not let me know and I'll provide what information you need