I started off by studying the letter distribution for a Bananagrams set, shown here:
And then I decided to compile a sampling of unbananagrammable words (leaving out some obscure or questionable ones), beginning with the letter...
Which word has more than three Bs? It appears in The Sound of Music. It's in a song (naturally). It's that "How do you solve a problem like Maria?" song. Answer: The word is flibbertigibbet, meaning a flighty person, and it's generally used in a critical fashion. I kind of like this word and vote that the nuns try to cut flibbertigibbets some slack.
There are about 100 words that would require more than three C tiles to construct, but most of them are highly technical, like "diplococcus" (a kind of bacteria) or compound words like "sacrococcyx" that have to do with things near or connecting to the tailbone. (As a corollary, you can make the word coccyx in Bananagrams (if you ever wind up with all 3 Cs).)
A concrescence is a collection of parts that have grown together, like a bunch of cells in a biological context. The verb meaning to grow together is "concresce".
My new favorite C-laden word is scacchic. It's a very obscure word meaning "pertaining to chess". And it is the shortest word in English that contains four Cs.
riffraff - The people who are to be kept out. Used in a dismissive fashion. Depending on who's using the word, the riffraff may contain flibbertigibbets.
Yes, we are already at K! The two common words with more than two Ks are kickback and knickknack (4 Ks!).
A third example is knickerbockers. Knickerbockers are short pants for men that come down below the knee, but not all the way down to the ankle. They have mostly gone out of fashion, but a variant of knickerbockers can still be seen as a part of the uniform worn by baseball players.
metagrammatism - This means the practice of forming anagrams. It more commonly goes by the term "anagrammatism".
mummiform - Shaped like a mummy. There are a lot of cool -iform words like "igniform", meaning shaped like fire and "cucumiform", meaning shaped like a cucumber.
whippersnapper - An inexperienced yet cocky kid. The term was originally coined to describe 17th-century slackers who hung out on the street, snapping whips for no reason. Somewhere along the way the meaning morphed to its current form. No thanks to the whippersnappers!
stresslessness has an amazing 7 Ss AND it is a word that people actually use sometimes.
possessionlessness, in contrast, seems a little unwieldy and virtually never appears in print. But it does have 8Ss, and that counts for something.
pizzazz is kind of amazing for being over 57% Z (not to mention 71% pizza). "Pizzazz" is the shortest word that you cannot spell with one set of Bananagrams tiles.
That's it! There are really very few words you can't spell with Bananagrams. And maybe a spell checker.