According to Merriam-Webster, there are two reasons that the reason . . . is because is incorrect: one of grammar and one of redundancy. They quote Bremer (1980) who explained the reasons as follows:

The grammatical reason for the error in “The reason he failed is because he didn’t study” is that the reason is calls for a nounal clause: “The reason he failed is that he didn’t study.” The adverbial conjunction because is correct in “He failed because he didn’t study.”

A simpler reason is that because means “for the reason that” and therefore one would be saying, “The reason he failed is for the reason that . . . .” which is as redundant as saying “The because is because.”

Merriam-Webster goes on to discuss that the grammarians created the grammatical explanation for why this particular phenomenon is wrong because they did not like the redundancy of it. Many renowned writers have used the phrase, including Jonathan Swift, Robert Frost, Ernest Hemingway, and even the great grammarian H. W. Fowler:

There is indeed no mystery about why people go wrong; it is because, if the thing had to be said without the use of the verb like, would, & not should is the form to use. —Fowler 1926, s.v. like v.

If the fellow who wrote it seems to know more of my goings and coming s than he could without complicity of mine, the reason is because he is a lovely old boy and quite took possession of me while I was in Boston. —Robert Frost, letter, 22 March 1915

Graph with reason is because percentage:

When we look at COCA, however, the frequency increases quite a bit. Whether this is due to current usage or spoken language being recorded is unclear, but either way the numbers do go up significantly.


Graph with all genres (because is blue):

Graph with percentages:

As is to be expected, the reason . . . is because occurs most frequently in spoken English according to the COCA. It is interesting to me, however, that it is higher in newspaper writing than in magazine writing; I would have expected the less formal the reason . . . is because to appear in more magazines as they seem to use more colloquial phrases than the newspapers do. However, I suppose this would take into account magazines such as the Economist, New Yorker, Newsweek, etc. which have more formal registers than People. Or perhaps the magazine editors have more time and are more conscious of this particular prescription than the newspaper editors.

A similar redundancy found in the language would be the reason is, is that/because. When searching for this in the COHA, it only appears once with the BE verb repeating itself immediately. However, in COCA it comes up a bit more; while it only has twelve tokens, the fact that they are all in the spoken register indicates that this phenomenon is really only occurring in speech: it appears once in COHA and all of its appearances in COCA were spoken in news broadcasts. This indicates, again, that people are not thinking through sentences while they are speaking. It also seems to be a slightly on the rise in the last few years, although as there are only twelve instances total that might not necessarily be accurate. Unfortunately, the fact is, is that/because is even more prevalent than the reason is, is that/because, with all hits in COCA in the spoken register again. There are no hits for it in the COHA.

When looking at the other to corpora, we see that TIME has 54 hits for the reason . . . is because, but none for the reason is, is that/because. The BNC has 206 hits for the reason . . . is because but none for the reason is, is that/because either.