Praise be to Allah.
Saying Qunoot in the obligatory prayers is prescribed when there is a reason for that -- which is when calamity is befalling the Muslims. So long as calamity is occurring, then Qunoot should be said for that, and when the reason is no longer present, then Qunoot should stop, because the Prophet (blessings and peace of Allaah be upon him) continued to pray Qunoot against the mushrikeen and to pray for the oppressed Muslims in Makkah for a month, then he stopped saying Qunoot when the reason for it stopped with the arrival of those for whom he had prayed Qunoot. This is indicated by the hadeeth of Abu Hurayrah (may Allaah be pleased with him) according to which the Prophet (blessings of Allaah be upon him) prayed Qunoot for a month. After saying Sami’a Allaahu liman hamidah, he said in his Qunoot: “O Allaah, save al-Waleed ibn al-Waleed, Salamah ibn Hishaam, ‘Ayyaash ibn Abi Rabee’ah and the weak and oppressed believers. O Allaah, punish Mudar severely and send upon them a famine like that of Yoosuf.” Then Abu Hurayrah (the Allaah be pleased with him) said that they were saved from the clutches of the kuffaar and came to Madeenah, so the Messenger (blessings and peace of Allaah be upon him) stopped praying for them. Narrated by Muslim (675).
Ibn al-Qayyim said: He prayed Qunoot at the time of calamity to offer supplication for some people and to pray against others, then he stopped when those for whom he had prayed came (to Madeenah) and were saved from captivity, and those against whom he had prayed became Muslim and came repenting. So his Qunoot was for a purpose, and when that was achieved he stopped Qunoot. End quote.
Zaad al-Ma’aad (1/272)
If the calamity is still ongoing and has not ceased, such as the occupation of Iraq for example, or the occupation of Palestine, then Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) stated that in this case it may be said that Qunoot may be offered for a month and then stopped.
And Allaah knows best.