Islam critiqued has a perfect memory; The prophet forgets the Quran?

In answer to the video "Perfect Preservation of the Quran is a Modern Invention"

As is explicit in the Quran, the divine protection of the prophets pertains strictly to the revelation and its implementation. But in everyday affairs, the messengers, who are still humans endowed with freewill and thus the potential, if not to sin due to their heightened level of spiritual awareness, to make mistakes, they are left to their own devices in their everyday lives to fight off the assaults of evil forces. 

No prophet was in a constant state of communication with the divine realm. The hadith and Quran itself speak of long periods where revelation had stopped, and the subsequent tauntings of his enemies on the issue, the questions of his followers and his anxious anticipation. The prophet is for instance reported, as a reflection of his all too often humble character, to have said

"I am only human like you; I forget as you forget. If I forget, then remind me".

This comes in the context of a slight mistake which he had done during prayer, inadvertently shortening it, apparently angry with himself as he suspected the mistake, then humbly accepting the correction from the attendance which confirmed his thought

"The Prophet (peace be upon him) meanwhile, stood by a piece of wood placed in the mosque, leaning against it, as if he was angry. So a man stood and said, 'O Messenger of Allah, have you forgotten or has the prayer been reduced?' So the Prophet of Allah (peace be upon him) said, 'I did not forget nor has it been reduced.' So the man said, 'Rather you have indeed forgotten.' So the Prophet (peace be upon him) said to the Companions, 'Is what he is saying true?' They said 'Yes' So the Prophet (peace be upon him) went forward and prayed what remained of the prayer, then he gave the salutation, then he prostrated twice, then he gave the salutation".

The prophet did not forget the Quran. He forgot, momentarily like any one with a memory lapse, certain passages. That is irrelevant to the issue of Quran preservation. When these memory lapses occured, the Quran had already been transmitted, in both oral and written form. Hence even regular members of the community, not even renouned memorizers, correcting the prophet's recital.

Something important noting in that regard. The Quran assures him

87:6"We shall make you recite (sanuqriuka) so you shall not forget".

Allah was literaly puting the holy words into the prophet's mouth

19:97"We have only made it easy in your tongue that you may give good news thereby to those who guard (against evil) and warn thereby a vehemently contentious people"

and teaching him how to read them out. As the prophecy of Deut18 says

"I will raise them up a Prophet from among their brethren, like unto thee, and will put my words in his mouth; and he shall speak unto them all that I shall command him".

Man is apt to forget, and the Prophet was a human being and he too was apt to forget and since the Quran was also a great asset which was being entrusted to him, he would repeat each and every word of the revelation fearing that any of it might slip away from his memory. This verse, telling him he will be made to recite in manner so as to not forget, came as a reassurance, stressing that God has taken upon Himself its impression on his memory. This was not by his own power and leave, being a mortal like anyone else and it is a reminder of this reality that the Quran continues

87:7"Except what Allah pleases, surely He knows the manifest, and what is hidden".

The context of the verse is about intricate, detailed, purposeful divine planing for all things and how nothing escapes God's grasp and knowledge. The prophet's rare occasions of very limited forgetfulness (and his followers and recorders' reminding him) were fully in accordance with that master plan, meant among other things at humbling him as well as to the believers' eyes around him, of his own faillibility as a human being as well of God's being in control of the process of memorization and compilation of the Quran, allowing only what He wills to be temporarily, not completely, forgotten.

As a principle, the Quran reminds in many instances of that concept, how this revelation and its very preservation is a mercy from Allah that could be taken away from Muhammad or erase parts of it from the prophet's own memory without him noticing it as said above, therefore man should remain grateful for it and never feel complacent

17:86-7"And if We please, We should certainly take away that which We have revealed to you, then you would not find for it any protector against Us. But on account of mercy from your Lord-- surely His grace to you is abundant".

It is because of  this very complacency towards divine guidance, the rejection, persecution and killing of the prophets sent in their midst that God temporarily interrupted an ongoing guiding revelation to the nation of Israel Ezek3:26,24:27,33:21-22.