Must prayers performed with a slight feeling of drowsiness be re-offered, knowing that the drowsiness was not overwhelming and out of fear of the prayer's time expiring?

If one of you feels drowsy during prayer, he should sleep until he knows what he is reciting. This applies generally to both obligatory and supererogatory prayers, whether at night or during the day. The reason for this is that drowsiness might lead the worshiper to revile himself without realizing it.