Why can't "thanks" ever be singular as a noun?

Solution 1:

Thanks is considered a plural noun, however used to denote one expression of gratitude. There is a transition in the history from the obsolete singular form to the current plural form.

In OED, the latest examples of the singular form is from the end of the thirteenth century and the earliest examples of the plural form is from the beginning of fourteenth century.

The latest example of the singular form is from the Haveloc the Dane, the second oldest surviving romance written in English. (1300, composition date):

Þus wolde þe theues me haue reft, But godþank, he hauenet sure keft.

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_{†Gode þank, God-thank [= Latin Deo gratias, French grâce à Dieu] , thanks (be) to God, thank God.}

There are also earlier usages like:

• Is this the thanke which you returne to God? (1642, D. Rogers, Naaman)
• He will thank you woman. M. M. I will none of his thanke. (a1556, N. Udall, Ralph Roister Doister)

The earliest example of the plural form is from the Ayenbite of Inwyt (a confessional prose work written in a Kentish dialect of Middle English, translation of the French Somme le Roi, 1340):

Me..him ne yeldeþ þonkes of his guodes, þet he ous heþ ydo.

OED also mentions that it was formerly sometimes construed as singular and we see an example from 1481, The History of Reynard the Fox (William Caxton's English translation):

All hath he but lytyl thanke.

According to OED, the current plural noun form first appears in Shakespeare's Titus Andronicus in 1594:

Thanks to men Of Noble minds, is honourable meede.

Another plural form appears in Shakespeare's Romeo & Juliet in 1599:

Else is his thankes too much.

Shakespeare might have an influence on the usage of the current plural form and the expression might have been used in that form till today. (there was a slightly different form thankes also as mentioned before).

On the other hand, there is also the usage a thank where thank is used in singular noun form. OED mentions that it is rare but not obsolete. It might be used mainly in literature and there is an example as late as 1849, from H. W. Longfellow's Black Knight:

The children drank, Gave many a courteous thank.

Finally, OED puts the following note below the obsolete sense of thank "Kindly thought or feeling entertained towards any one for favour or services received; grateful thought, gratitude. Rarely in pl."):

The sense of ‘gratitude, kindly or loving feeling for favour or benefit’ must have been developed between that of ‘good will, good feeling’ generally, and that of ‘the expression of gratitude’. But the feeling passes so naturally into its expression that it is not easy to separate them in the quotations, except by the accompanying verbs: to express one's thanks, and the archaic to con thanks, ought to mean to express one's feelings of gratitude; but to give, offer, return or receive thanks, ought to mean to give or receive the expression of gratitude; so to have thanks, but this is less clear. In many instances it is impossible to say which is meant...

Solution 2:

The simple answer to the OP is that it's a fixed expression because we've said thanks that way for many centuries:

Old English þanc, þonc in late use "grateful thought, gratitude," plural form thanks from mid-13c., from the same root as thank (v.). Compare Old Saxon thank, Old Frisian thank, Old Norse þökk, Dutch dank, German Dank.
The Old English noun originally and chiefly meant "thought, reflection, sentiment; mind, will, purpose;" also "grace, mercy, pardon; pleasure, satisfaction."

As short for ‘I give you thanks’ from 1580s; often with extensions, such as ‘thanks a lot’ (1908). Spelling thanx attested by 1907.
emphasis mine

In the etymology of the verb thank we notice a relationship to think:

Old English þancian, þoncian "to give thanks, thank, to recompense, reward," from Proto-Germanic *thankojan
(cognates: Old Saxon thancon, Old Norse þakka, Danish takke, Old Frisian thankia, Old High German danchon, Middle Dutch, Dutch, German danken "to thank"),
from *thankoz "thought, gratitude," from PIE root *tong- "to think, feel."

Related phonetically to think as song is to sing; for sense evolution, compare Old High German minna "loving memory," originally "memory."
Related to Old English noun þanc, þonc, originally "thought," but by c. 1000 "good thoughts, gratitude."
In ironical use, "to blame," from 1550s. ‘To thank (someone) for nothing’ is recorded from 1703.
emphasis mine

It is safe to assume that gratitude produces an ongoing series of thankful thoughts as benefits resurface over time. Looking back, thanks acknowledges many grateful thoughts. Looking forward, it foresees many grateful thoughts.

After almost 45 years, I haven't forgotten the kindness Mr. Shellinger, my sixth grade teacher, showed me. I have enjoyed many thankful thoughts of him over that time, and I don't suspect them to cease:

Thanks Mr. S!