Master Brahma once asked all the three siblings Ravana, Vibhishana, and Kumbhakaran for a desire. Being very much aware of Kumbhakaran's mind and courage, Indra mentioned Goddess Saraswati to tie his tongue, on account of which Kumbhakaran requested the desire of endless rest. 

Ravana couldn't see his sibling's predicament and subsequently argued Lord Brahma to reclaim his sibling's desire. Master Brahma couldn't fix the whole wish, however he said that Kumbhakaran would rest for a large portion of a year and will remain wakeful for the other half. 

During the fight with Rama, Kumbhakaran was snoozing, and numerous endeavors were made to wake him up.