To be suddenly overcome by strong sleepiness; to be on the verge of falling asleep.
長い会議中、睡魔に襲われてこっくりしてしまった。
During the long meeting I was overcome by sleepiness and nodded off.
授業中に睡魔に襲われると集中できないから、しっかり寝てから来てね。
If you get overcome by sleepiness during class you can't concentrate, so make sure you sleep well before coming.
夜更かしした翌日は、電車で睡魔に襲われることが多い。
The day after staying up late, I'm often overcome by sleepiness on the train.