Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.
As to what follows:
In response to your question, we say, and with Allah Almighty lies all success:
I have not come across this du`a in what I have reviewed of the books of hadith, nor of what has been narrated from the Salaf of the Ummah and their Imams. However, what appears to me is that the one making such a du`a is asking Allah to not do something to him in the future that he dislikes. Similar to this in meaning has been mentioned in du`as mentioned in Allah’s Book and in the Sunnah. Among these is Allah Almighty’s statement:
“Our Lord, and grant us what You promised us through Your messengers and do not disgrace us on the Day of Resurrection. Indeed, You do not fail in [Your] promise.” [Aal `Imran 3:194]
And Ibrahim’s statement in his du`a:
“And do not disgrace me on the Day they are all resurrected.” [Al-Shu`ara 26:87]
And it is mentioned in the end of Surah al-Baqarah:
“Our Lord, do not punish us if we have forgotten or erred.” [Al-Baqarah 2:286]
Also, from among these is the du`a of the Prophet (peace be upon him) when he would pray over the dead body in Janazah, from the hadith of Abu Hurayrah (may Allah be pleased with him), “O Allah, do not deprive us of his reward, nor cause us to go astray after him.” [Tirmidhi and others]
This is quite frequent in the Qur’an and Sunnah. As such, there is nothing wrong with this, and it is among the prescribed meanings used in du`as. However, making du`a using this phrase, “May Allah not have decreed it,” is different to what we have mentioned thus far, from the angle that it is asking Allah to not have done something, not asking Him to not do something. There is a difference between the two, as asking Allah to not have done something is something that I do not recall any evidence for, nor do I know of it having been mentioned anywhere after some research. Furthermore, asking for something of this meaning is something that the Sunnah has proven to be unprescribed due to there being no benefit to it. When Umm Habibah (may Allah be pleased with her) said, “O Allah, enable me to derive benefit from my husband the Messenger of Allah (peace be upon him), from my father Abu Sufyan and from my brother Mu`awiyah,” the Prophet (peace be upon him) said, “You have asked from Allah about durations of life already set, the length of days already allotted and the sustenances the share of which has been fixed. Allah would not do anything earlier before its due time, nor would He delay anything beyond its due time.” [Muslim 2663]
So what appears to be the case is that making du`a using this phrase should be abandoned, and instead one should ask Allah to ward off a particular harm and disliked matter.
And Allah Almighty knows best.