嚔 is indeed hard to produce, even for Chinese native speakers. It is an example of an exception, though, like entrepreneur in English (I know it is from French, so the spelling is "unusual").

First, people don't write 喷嚔 often, although they use it in spoken Chinese regularly. It seems people are reluctant to write down words that describe certain body functions.

For 嚔, the difficulty is that its "sound" component is extremely rare in Chinese characters. The majority of Chinese characters are 形声字. Each of such character has a "sound" component and a "meaning" component. Many characters can share the same "sound" component. The "sound" components are usually the "harder" component in writing, in that they have more strokes. (For 嚔, the rectangle at the left is the "meaning" component. The complicated looking part at the right is the "sound" component.) As a result, if one remembers how to write one character, one can simply remember many other characters with the same "sound" component. If one of these characters is commonly used, it is an easy task to remember all the others.

I only know two other characters who share the same "sound" component with 嚔, and I don't think people use them now. They only appear in ancient books.

So 嚔 is a character you don't often write down, and there are no other commonly used characters who shared the same "sound" component. Then you get a character who is hard for native Chinese speakers as well.