You are allowed to make Istighfaar as often as you can without any inhibition except at the expense of the prescribed supplications in Salah.
When it comes to Prayers, we may do well to follow the manner and method of the Prophet as closely as possible unless we have evidence indicating latitude or flexibility.
The Prophet (peace be upon him) said, “Pray as you saw me praying.” Thawban, one of the close companions of the Prophet (peace be upon him) said, “It was the habit of the Prophet to make Istigfaar ( by saying Astaghfirullah) three times upon finishing the Prayer: he would then add the following words:
Allaahumma antha al-ssalaam wa minka al-ssalaam tabaaraktha yaa dhal jalaali wa al-ikraam
(O Allah, You are (the source of) Peace, and the peace is a gift from you; You are the exalted, O the possessor of mighty and glory).
Therefore, we should do the same after performing the obligatory prayers.
Now the question arises: are we allowed to do the same after voluntary prayers? According to the majority of scholars, it is not prescribed; however, there is no reason to forbid it, if a person were to do so; it cannot be condemned or disapproved.
We have ample evidence in the sources to show it is desirable for us to do so after every act of worship or good deed we perform:
Allah says,
And when you pour forth Arafat, remember God at the holy place, and remember Him as He has guided you after you had been astray; and pour forth together with the people who pour forth, and ask forgiveness of God for your sins: for, verily, God is Forgiving, Merciful.” (Al-baqarah 2:198-199)
Istighfaar after performing acts of worship is intended to ensure that our good deeds are acceptable; for as humans no matter how focused we are we may be deficient in so many ways that we are not unaware of. That is why even the great prophets, Ibrahim and Ismael, turned to God praying to Him for acceptance and forgiveness upon completing the rebuilding of the Kabah.
Therefore, Istighfaar, in general, is prescribed after prayers as well as all other acts of worship such as fasting, zakah, and Hajj and any other good works we may do.
Furthermore, the Prophet (peace be upon him) also said, “Whoever clings to Istighfaar as a habit, Allah will appoint for him or her a way out of all troubles and hardships and provide sustenance for them in ways they would never be able to imagine.”
So, never mind what people say. You are allowed to make Istighfaar as a habit except at the expense of specific supplications that are prescribed on special occasions or circumstances.
Almighty Allah knows best.
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