Miswar bin Makhramah (may Allah be pleased with him) came to Sayyiduna Umar bin al-Khattab (may Allah be pleased with him) after the incident, on the night in which Sayyiduna Umar (may Allah be pleased with him) had been stabbed with a dagger; he had led the morning prayer. Sayyiduna Umar (may Allah be pleased with him) was woken and told: The morning prayer! Sayyiduna Umar (may Allah be pleased with him) said: "Yes! Whoever abandons the prayer has no share in Islam." Sayyiduna Umar (may Allah be pleased with him) prayed while blood was flowing from his wound.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحيض / 1673
Sayyiduna Ikrimah (may Allah be pleased with him) says concerning a nosebleed that does not stop: he should block his nose, then perform ablution and pray.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحيض / 1674