I am sleep deprived most nights. My son wakes up several times a night. Most my efforts to have a doze during the day while my son is sleeping are TO no avail.
I noticed THAT when he sleeps on my belly, he tolerates bouts of colic easily , AND that's why I put him TO sleep with his tummy on my tummy, and that's ALSO why I usually don't fall asleep till two am.
To not avail = ineffective , unsuccessful.
Of no avail = not effective , of no use