Englishgrammar.org has an article discussing cases where an infinitive does not use the word "to." One case is with many causative verbs like "make" and "let."
I want the water to run
*I want the water run
I make the water run.
*I make the water to run.
It is also the case with "perception" verbs.
I see the water run.
I hear the water run.
The site describes "help" as a special case that can be followed by an infinitive either with or without "to."
She helps me stand.
She helps me to stand.
My question, essentially, is why "help" is a special case that can either ellipse the "to" or not, and what the semantic implications of that choice are?
My hunch is that since one category of other verbs that do not require a "to" infinitive are causative, the choice of whether or not to include "to" has a semantic bearing on whether the subject in the sentence is perceived as a causal agent.
So in the example, "she helps me [to] stand," we would infer from the inclusion of "to" that the subject (she) is less of a causal agent than when "to" is excluded.
It seems possible that there are no broadly applicable implications from the inclusion or exclusion of "to" in an infinitive following "help," that perhaps it is an aberration by way of etymology or coincidence, but I've been unable to find sources that analyze the case beyond identifying it as an outlier.
Best Answer
Made in America
In the Google Books corpus of American publications, the construction help + bare infinitive, an American innovation, overtook its older equivalent with the marked infinitive around 1982 and has since skyrocketed in frequency. In Britain, help+BI, often still termed an Americanism or “informal usage,” is now favored by a substantial number of native speakers, though by a far less percentage than across the Atlantic.
Source: McE-X 2005, 164.
This construction is indeed an American innovation and a rather early one. Only eighteen years after the Declaration of Independence the first usage of help+BI appeared in an American newspaper:
Further examples are sparse until a flurry in the late 1830s, almost exclusively from Vermont:
By the mid-1840's, newspaper writers across the country were using the construction, but unless Rep. Wise of Virginia spent considerable time in New England unknown to historians, assigning an origin to this region remains only a tantalizing possibility.
Pro-verbs, Pronouns, and the Passive
The use of the marked infinitive is strongly favored even in America when the dependent verb is the pro-verb do:
Nevertheless, there are educated native speakers who choose the bare infinitive:
The marked infinitive is obligatory when it is the antecedent of the dummy subject it:
But not when the pronoun has a real antecedent:
The marked infinitive is also obligatory when help is in the passive voice:
Need, Dare
The verbs need and dare have been considered at least semi-modals in taking a bare infinitive.
Dare is interesting in that while "He dare not go" sounds like a line in a bad nineteenth century melodrama, "Would you dare say that to him?" has no such allusions and is quite current and can be used both with and without the infinitive marker. This usage most closely parallels that of help.
It's all semantics
A rapid rise in usage of help+BI does not suggest large numbers of Americans discovering a long lost sense of to help and suddenly applying it in everyday speech. Nevertheless, some have attempted to tease apart some semantic distinction between the two uses. One scholar suggests this minimal pair [McE-X 2005, 170]:
The distinction that while Mary helped John by eating a share of the cake, she actively helps John perform an action himself, even if she's doing all the work.
For the first "no leftovers" option, there are plenty of examples:
And also for the second:
Unfortunately, however, war, accident, and debilitating disease have left many Americans unable to do basic tasks without help, and they have described their experiences with the favored construction:
The supposed distinction evaporates.
Conclusion
The modern usage of help offers two choices of dependent infinitive construction: the bare or marked infinitive. The choice of one over the other is solely a stylistic choice for speakers of American English, and today, most likely for British speakers as well. The choice oftens seems arbitrary:
There is no possible reason for choosing one infinitival form over another except the writer's choice.