Has there ever been a significant security breach of information from someone with Alzheimer's or dementia divulging classified information?

Many 'cases' of dementia are never diagnosed, many 'cases' are kept secret—for a while at least.

One example for 'keeping that secret of dementia' and perhaps overlapping with 'not diagnosed (yet)' might be former President Ronald Reagan:

In a 2011 book titled My Father at 100, Reagan's son Ron said he had suspected early signs of his father's dementia as early as 1984;[356][357] an allegation that sparked a furious response from his brother, Michael Reagan, who accused him of "selling out his father to sell books".[358] Ron would later temper his claims, telling The New York Times he did not believe his father was actually inhibited by Alzheimer's while in office, only that "the disease was likely present in him", for years prior to his 1994 diagnoses.

That illustrates quite well, regardless of 'when' the disease eventually degraded far enough to be of concern for this type of question. A 'demented state' of mind is not equal to a proper diagnosis, and even the actual diagnosis falls onto a spectrum of decline, with early diagnosis quite certainly a matter of some debate in most cases.

While some might hold the quite controversial opinion that other presidents 'were suffering from early forms of dementia, even from the point of taking office', whether they were indeed in 'enough decline' for a proper diagnosis seems undebatable for others.

President Trump proudly proclaimed to have a 'test for dementia' administered to him. Which he said he had passed. Albeit not with too much convincing words he addressed at the public about that.

Others saw him at that point as 'clearly suffering', his former ally Bannon or newspapers.

As long as one accepts the possibility of Trump checking all the boxes for such a classification, then he did 'talk too much' — and certainly inadvertently at the time — about military operations and US allies involved in those:

President Donald Trump discussed classified information provided by a U.S. ally regarding a planned Islamic State operation during an Oval Office meeting on May 10, 2017 with the Russian Foreign Minister Sergey Lavrov and the Russian Ambassador Sergey Kislyak, providing sufficient details that could be used by the Russians to deduce the identity of the ally and the manner in which it was collected, according to current and former government officials.

With this rather recent example chosen to mainly illustrate the difficulties arising from applying this medico-psychological or psychiatric side of things: many 'secrets' have a shelf-life. They need to 'stay secret' for a while, and when a former holder of classified information gets old enough to also display such signs of dementia, the information potentially declassified under such circumstances might be in quite many cases too old as well to be still 'relevant'. Further, when someone is obviously suffering from dementia, any such information's reliability will be called into question from the get-go, and with most forms of actual dementia the bigger problem might be seen in actual information being present somewhere in the sufferer's memory, but inaccessible — thus turning interesting memories into actual secrets under a firmer lock than previously.

Almost Certainly No

While one can never rule out activity done covertly by governments, there doesn't appear to be anything readily accessible indicating an elderly person/s divulged classified information in a way that caused a security leak. The reason for this seems apparent if you consider the various likelihoods.

1: Lets say a gentleman named Joe has worked on Project X for 10 years, and retires at 65 in relatively good health. By age 70 he has signs of dementia, and by 75 has full-on "lost it" for want of a better term. Say he retired in 2010, so between 2015 and 2020 he's "going" and after 2020 he's "gone". Project X started in 2000, and he was there for the entire first 10 years.

2: Now lets say the Chinese really want information about Project X. They've known of it since about 2003. What are they doing to get that information? they're trying to hack government databases, they're trying to ID employees who are working on it and see if they can flip them/insert people into the project etc etc.

They know Joe worked on the project. Crucially though, they EITHER get him to give them intel while he works there, tried to convert him and failed, or leave him be as not a likely candidate. Once Joe retires the Chinese are unlikely to keep monitoring him, because they only have a certain amount of personnel and a certain amount of time to devote to Project X, and those resources are into Joe's replacement who has real-time intel on the project. They're simply not going to waste time keeping tabs on Joe to the point where they can monitor his potentially-degrading mental health. It's just not a good use of resources.

But let's say that for whatever reason the Chinese DO find out Joe's mind is going... now what? They can't be certain his dementia is at the magic point where he'll tell them everything they want to know AND remember it well enough to be useful. Do you risk a well-placed spy wandering into an old folks home where they have no business being just to talk to a guy who might be more interested in finding his remote for the 100th time than talking government secrets? Do they even HAVE a spy with the training to coax a dementia patient into talking about a subject? How much can you trust the intelligence he's giving you? After all, he's got dementia and there's no telling whether he's lying or simply conflating Project X with memories of his Eagle Scout project. Do you really want to tell your boss you ran a high-risk op for information you can't say is from a reliable source because the source's brain is going? And after that, then what? Is it worth risking Joe telling his son a nice man came and talked to him about Project X? Do you risk follow-up visits? What if he's having a period of lucidity? THAT could go very badly.

At the end of the day it would be a criminal misuse of resources. You'd be infinitely better off putting all the time/effort into identifying and "interviewing" dementia patients whose intelligence is by default going to be years out of date into getting up to date access via more traditional means.