Abu Azzah was captured in a previous war between the Muslims and pagans. When he was captured, he begged Prophet Muhammad (p) to show mercy and let him go. The Prophet (p) out of kindness and mercy released him on the condition that he does not take arms against the Muslims again.

Abu Azzah promised not to engage or attack the Muslims. However it did not take long before he joined battles again, against the Muslims. Hence, he was captured a second time, and was killed.

Tabari:

Abu Azza Amr b. Abd Allah al-Jumahi had been treated kindly by the Messenger of God on the day of Badr, being poor man with daughters. He was among the captives, and he said, ‘ O Messenger of God, I am a poor man with a family and with needs which you are aware of, so treat me kindly, may God bless you!’ 

The Messenger of God then treated him kindly. Safwan b. Umayyah now said, ‘Abu Azzah, you are a poet, so aid us with your tongue, and join our expedition.’

Muhammad has treated me kindly,’ he replied, ‘and I do not wish to help against him.’ ‘No,’ he urged, ‘aid us in person, and I swear before God that if you return I will make you a rich man and that if you are killed I will treat your daughters as I treat my own daughters, whatever hardship or prosperity comes my daughters’ way will come their way.’

With this assurance, Abu Azzah joined the expedition, travelling through Tihamah and calling upon the Banu Kinanah. Similarly, Musafi B. Abd Manaf b. Wahb b. Hudhafah b. Jumah went to the Banu Malik b. Kinanah to rouse them and call upon them to fight the Messenger of God. [1]

Safiur-Rahman Mubarakpuri

After the arrival of the caravan on Sunday, the Messenger of Allah stayed at Hamra Al-Asad for three days- Monday, Tuesday and Wednesday – 9-11 Shawwal, 3 A.H. and then returned to Madinah. Before his return, he took Abu Azza Al-Jumahi as a prisoner of war.

Incidently, this man had also been captured at Badr but on account of his poverty, and the large family he supported, the Prophet had been gracious enough to release him on condition that he would not involve himself in war against the Muslims again.

Abu Azza did not keep to his promise and took part in Uhud hostilities on the side of the polytheists. Here again he implored Muhammad for pardon but the latter told him that a believer wouldn’t be taken twice in the same snare. He then deservedly merited the sentence of death which was executed by Az-Zubair or, in another version, by Asim bin Thabit. [2]

Hisham M. Ramadan

Generosity may or may not be conditional. If it is, the prisoner will have to abide by the condition set forth in his case. The Prophet at the battle Badr freed a poet called Abu Azzah after the latter had given a formal promise never to join anyone who is fighting the Prophet. But Abu Azzah joined the polytheists in the Battle of Uhud and was taken prisoner by the Muslims. [3]

Cheragh Ali

ABUL OZZA
Abul Ozza, one of the prisoners of Badr, was allowed his freedom without any ransom on the condition that he would never again bear arms in any war against the Prophet; but he proved a traitor. He exhorted the Arabs to make war on Mohammad, and joined himself the invading army of Mecca. He was doomed to misfortune, he was caught at Hamra, and duly executed. This was in full accordance with the laws and usages of war (Vide ante, para 58). [4]

References:

[1] The History of al-Tabari: The Foundation of the Community: Muhammad At Al-Madina, volume 7, page 106
[2] Ar-Raheeq Al-Makhtum: The Sealed Nectar – Biography Of The Noble Prophet By Safiur-Rahman Mubarakpuri, page 291
[3] Understanding Islamic Law: From Classical to Contemporary By Hisham M. Ramadan page 85
[4] A Critical Exposition of the Popular Jihad (Original 1885) – Cheragh Ali page 81