Yes, longer exposure does lead to a stronger prime. The type of prime, supraliminal versus subliminal, may also impact strength.

Try

Dijksterhuis, A., & van Knippenberg, A. (1998). The relation between perception and behavior or how to win a game of Trivial Pursuit. Journal of Personality and Social Psychology, 74, 865-877.

or

Higgins, E.T., Bargh, J.A., Lombardi, W. (1985). Nature of priming effects on categorization. Journal of Experimental Social Psychology, 11, 59-69.

Thanks a lot!

Longer exposure to a prime does not necessarily lead to a stronger prime.

This is inherent in the nature of priming. Priming is a process by which information presented at an earlier time influences the processing of information presented at a later time. Therefore, when the information influenced by the priming information has been processed, the prime has had its effect and further exposure to the prime will not increase its effectiveness.

Consider the general process of semantic priming in language comprehension. The semantic content of Word 1 will influence the comprehension of Word 2 at a varying strength that depends upon the relationship between the two words within the more general context. But Word 2 will be processed very swiftly. In spoken language rates of 5-7 words per second are common, in reading faster rates are common depending on the nature of the material and the existing knowledge of the reader. So the semantic priming of Word 1 will be over in a few hundred milliseconds or less.

Longer exposure to the prime may have a negative effect. A "strong" prime is one that facilitates processing of subsequent information to a greater extent than weaker primes. A strong prime in language comprehension would be one that increases the speed of comprehension. Its duration of impact will be shorter than that of a weaker prime because that is the desired effect of the prime, to improve processing speed.

Longer exposure to a prime may mean two things. First, the prime may be the only task-relevant information presented for the duration of the prime. For fluent actions such as language comprehension, this will become disruptive as it slows the presentation of the fuller linguistic content to a point where it is below normal processing speed. This may result in deficient comprehension as the information presented is no longer linked in an optimal manner by the delay separating the components leading to comprehension. At a certain point, this will become conscious and the person will engage in other mental processes such as wondering why the information is being presented at such a slow rate or what to have for lunch.

Alternatively, the prime may remain in the immediate context for a relatively long duration while additional information is also present. A common example would be reading. The first word on a page is there for the entire existence of the page in an intact form. Less abstractly, the first word on the page is present while the entire page is being read. But it is processed and the reader moves along to the next, and the next. It is no longer an element of working memory/attention.

Again, things can be done to alter this, such as presenting the reading material on a computer screen and having the prime word follow the reader's gaze so that it remains in the foveal area for the entire reading time. This will also be something that soon becomes an impediment to the goal of reading comprehension. Less artificially, you may have experienced distracting influences of words that are given additional features that distinguish them from the major portion of the text, such as being put in bold font, highlighted, or in a different color. If the goal is reading comprehension and these characteristics attract more attention than is necessary to comprehend them, comprehension for the rest of the content may be slowed or diminished.

Moving beyond language, to things such as the background images on a website, the question remains, what is the prime for? The prime is intended to facilitate information processing. The prime will have an effect until that facilitation has been accomplished and the relevant information is processed. Beyond that, there's nothing to prime.

This again leads to information that is presented longer than necessary, or that is distinguished in a manner that distracts from other goals. With regard to the priming effects of the background images of a website, what are the images intended to prime? That will determine the useful lifespan of the images as primes. Beyond that, the information will be included in the greater context of the mental situation model created by the webpage, or it will be ignored for other content, or it will be a distraction from other content.

And I haven't read Dijksterhuis, A., & van Knippenberg, A. (1998). But I know the way to win at Trivial Pursuit: know the answers to most of the questions. If you can do this, you can join a game at the point where the people playing from the start have 4-5 pieces of their pie filled in and still win. This is also a good way of avoiding having to play Trivial Pursuit, since you make it no fun for anyone else. And that is fine with me, because when you know the answers, it's not so much fun for you, and it is certainly not fun to spend most of your time waiting for the other players to go through their turns trying to figure out whether their brains contain the answers. In effect, the distorted durations of events that are intended to prime fun are either too short or too long to do so.

And I'm going to guess that Higgins, E.T., Bargh, J.A., Lombardi, W. (1985) considered the completion of the categorization task as the activity to be primed, and were examining the effect of prime duration on accuracy and/or speed of performance on the categorization task. They probably also limited the prime durations to those measurable in seconds rather than minutes or hours. To do otherwise would turn the experiment from one examining priming to one dealing with the impact of presentation of task-relevant information contained in long-term memory for variable amounts of time upon performance of that task rather than one of priming.

But that may actually be what you are looking for with regard to content presented on webpages, such as advertisements that are not expected to result in an immediate click-through but instead impact decision-making after a rather long delay.

If so, you are more likely in the realm of research on persuasion than research on priming.

Thank you for this wonderful answer! I read it and read it again. Thank you for making many distinctions of terms with such clarity. This truly helped.