Use of “ever” in non-negated sentence

Is the sentence grammatically correct:

I do recall ever seeing my mother in the light of day.

Solution 1:

No, it's not grammatical. It violates the rule of English grammar that forbids use of a Negative Polarity Item outside a negative context.

From the article on "Negatives and Negative Polarity" in The Cambridge Encyclopedia of the Language Sciences:

[English has] a large, complex, and diverse system of Negative Polarity Items (‘NPIs’ – like ever in He didn’t ever see it), which felicitously occur only in the scope of some negative element (*He ever saw it). The details of what ‘scope’ actually is, and of how and which and why NPIs can occur within it, vary among specific negative and NPI elements.

Negative polarity is a variety of ‘negative concord’ (e.g French Je ne regrette rien, lit.‘I don’t regret nothing’; Yiddish Ix hob nit kin gelt, lit. ‘I don’t have no money’), but instead of negative concord, which uses negative elements in the focus of another negative, negative polarity uses other, non-negative elements, which can sometimes pick up ‘negativity by association’ and occur without overt negative (could care less < couldn’t care less).

‘NPI’ is a term applied to lexical items, fixed phrases, or syntactic construction types that demonstrate unusual behavior around negation. NPIs might be words or phrases that occur only in negative-polarity contexts (fathom, in weeks) or have an idiomatic sense in such contexts (not too bright, drink a drop); or they might have a lexical affordance that only functions in such contexts (need/dare (not) reply); or a specific syntactic rule might be sensitive to negation, like Subject-Verb Inversion with Adverb Fronting in

Never have I seen such a thing

*Ever have I seen such a thing.

*Frequently have I seen such a thing.

Ever is the suppletive word that English uses instead of the nonexistent *anywhen. Like any and all its other compounds, it's an NPI. Using an NPI without negation in a sentence produces an ungrammatical sentence [an asterisk before a sentence indicates that it is ungrammatical], e.g:

*He has arrived yet.
*I like that at all.
*He bothered closing the door.
*She's all that smart.
*This will take long.
*I know but what he's right.
*I can help thinking of how she looked.

Solution 2:

I do recall ever seeing my mother in the light of day.

A legal reading of that sentence is one in which ever here means always, as ever and anon it is wont to do. Wherefore given that this sentence is clearly grammatical:

I do recall always seeing my mother in the light of day.

Then so too must needs the original also be grammatical.

‘Ever he clutched me, and ever I hewed him...’

Here for your delectation are a handful of illustrative quotes from an obvious source:

Tonight the Lord of the Eagles was filled with curiosity to know what was afoot; so he summoned many other eagles to him, and they flew away from the mountains, and slowly circling ever round and round they came down, down, down towards the ring of the wolves and the meeting-place of the goblins.
That is why they were now riding in silence, galloping wherever the ground was grassy and smooth, with the mountains dark on their left, and in the distance the line of the river with its trees drawing ever closer.
It was difficult to get them to understand, what with their dizzy heads, and the shouts, and the whacking of sticks and the throwing of stones; but at last Bilbo felt he could delay no longer — the spiders were drawing their circle ever closer.
With such gloomy thoughts, followed ever by croaking crows above them, they made their weary way back to the camp.
Then they marched and gathered by hill and valley, going ever by tunnel or under dark, until around and beneath the great mountain Gundabad of the North, where was their capital, a vast host was assembled ready to sweep down in time of storm unawares upon the South.
Not that I venture to disagree with Thorin, may his beard grow ever longer; yet he was ever a dwarf with a stiff neck.
And in those days also they forgot whatever languages they had used before, and spoke ever after the Common Speech, the Westron as it was named, that was current through all the lands of the kings from Arnor to Gondor, and about all the coasts of the Sea from Belfalas to Lune.
Heavy have the hearts of our chieftains been since that night. We needed not the fell voice of the messenger to warn us that his words held both menace and deceit; for we knew already that the power that has re-entered Mordor has not changed, and ever it betrayed us of old.
But Gandalf bade us hope still for his cure, and we had not the heart to keep him ever in dungeons under the earth, where he would fall back into his old black thoughts.
Fear was ever in my heart for my friends in the Shire; but still I had some hope.
Ever as I came north I heard tidings of the Riders, and though I gained on them day by day, they were ever before me.
In here it is ever dark; but outside the late Moon is riding westward and the middle-night has passed.
In this high place you may see the two powers that are opposed one to another; and ever they strive now in thought, but whereas the light perceives the very heart of the darkness, its own secret has not been discovered.
‘As he ever has judged,’ said Aragorn.
‘We fought far under the living earth, where time is not counted. Ever he clutched me, and ever I hewed him, till at last he fled into dark tunnels. They were not made by Durin’s folk, Gimli son of Glóin. Far, far below the deepest delving of the Dwarves, the world is gnawed by nameless things. Even Sauron knows them not. They are older than he. Now I have walked there, but I will bring no report to darken the light of day. In that despair my enemy was my only hope, and I pursued him, clutching at his heel. Thus he brought me back at last to the secret ways of Khazad-dûm: too well he knew them all. Ever up now we went, until we came to the Endless Stair.’
You have ever been a herald of woe.
And ever men looked northward, asking: ‘Where are the Riders of Rohan?’
‘It is not to be wondered at: webs of deceit were ever woven in Dwimordene.’
In Dwimordene, in Lórien / Seldom have walked the feet of Men, / Few mortal eyes have seen the light / That lies there ever, long and bright.
For many the sound of the voice alone was enough to hold them enthralled; but for those whom it conquered the spell endured when they were far away, and ever they heard that soft voice whispering and urging them.
‘So we always do.’ he said, as they sat down: ‘we look towards Númenor that was, and beyond to Elvenhome that is, and to that which is beyond Elvenhome and will ever be.’
Ever your desire is to appear lordly and generous as a king of old, gracious, gentle.
Ever they circled above the City, like vultures that expect their fill of doomed men’s flesh. Out of sight and shot they flew, and yet were ever present, and their deadly voices rent the air.
Have we not heard of thee at whiles, and of thy wanderings, ever hatching plots and mischief at a safe distance?
The Road goes ever on and on / Out from the door where it began.

Solution 3:

It's not ungrammatical; just a little unusual, maybe a little poetic even. If English is your second language, I would recommend avoiding this construction.

I would interpret "ever" as meaning the same as "always" in this context; that is, I always saw my mother in the light of day. It could indicate, for example, that whenever it was daytime, she was there checking up on me.

Solution 4:

This can only be said in sarcastically echoing a question, "Do you recall ever seeing ...", in a positive assertion.

This may be a literary technique, but is not grammatical as far I can say off hand.

Solution 5:

"I do recall ever seeing my mother in the light of day" would seem like a tautology to me.

"I do not recall ever seeing X" is a way of saying "I do not recall seeing X at any time in the past"

Saying "I do recall ever" means something like "I do recall at any time" which is self-evident from the fact of remembrance. If you do remember it, it must have been at a time in the past, therefore to say "ever" in this context is to repeat oneself in a rather confusing fashion.

Is it strictly grammatical? I don't think so, at least in so far as by using a word that adds nothing to the sentence but simply repeats a meaning already expressed is always better avoided.