Prayer is not invalidated by flowing blood

Sayyiduna Jabir bin Abdullah (may Allah be pleased with him) narrates: We set out with the Messenger of Allah (peace and blessings be upon him) on the expedition of Dhat al-Riqa'. There a Muslim man harmed the wife of a man from the polytheists. When the Messenger of Allah (peace and blessings be upon him) set off on the return journey, the woman's husband came back, and when he learned what had happened he swore that he would not rest until he had shed the blood of the Companions of the Messenger of Allah (peace and blessings be upon him). So he set out following the Prophet (peace and blessings be upon him). The Messenger of Allah (peace and blessings be upon him) halted at a place and asked: "Who will guard us tonight?" A man from the Muhajirun and a Companion from the Ansar said: "O Messenger of Allah! We are at your service." He (peace and blessings be upon him) said: "The two of you guard the mouth of the valley pass." When the two of them reached it, the Ansari asked the Muhajir which part of the night he would like him to take on for him. He said: "Rather, take the first part for me," and he lay down and slept, while the Ansari Companion stood up to pray. Meanwhile, the woman's husband arrived there. When he saw the figure of a man, he shot an arrow which struck the Ansari Companion. He pulled it out and remained standing in prayer. The man shot a second and then a third arrow; he pulled those out too and continued his prayer. Then he bowed (ruku'), woke his companion and said: "Get up, I have been wounded." When the man saw the two of them, he fled. When the Muhajir Companion saw the Ansari covered in blood, he asked: "Why did you not wake me at the first arrow?" He replied: "I was reciting a surah and did not want to end it without completing it. When he kept shooting at me, I bowed and informed you. By Allah! Were it not for my fear of losing the post that the Messenger of Allah (peace and blessings be upon him) commanded me to guard, my life would have left me before I completed the surah, and I would not have broken off the prayer."
This hadith has a sahih (authentic) chain, and Imam Muslim used Muhammad bin Ishaq as evidence. This hadith establishes that blood flowing from other than the passages of ritual impurity does not break ablution.

A similar narration is reported from Sayyiduna Jabir bin Abdullah (may Allah be pleased with him) from the Prophet (peace and blessings be upon him).

Sayyiduna Abu Sa'id al-Khudri (may Allah be pleased with him) narrates that the Messenger of Allah (peace and blessings be upon him) said concerning two people talking to each other while relieving themselves: "Allah Almighty is intensely displeased with this act."