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According to the Merriam-Webster online dictionary, both undiscoverable and indiscoverable are valid adjectives, and indiscoverable deserves a web page of its own: http://www.merriam-webster.com/dictionary/indiscoverable

In https://en.oxforddictionaries.com/search?utf8=%E2%9C%93&filter=noad&query=indiscoverable, indiscoverable is not mentioned, while undiscoverable has a web page only in BrE.

So, these two sources contradict each other somewhat. Which adjective is the right one in AmE?

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Indiscoverable is a word, but it was never a common one, and it is getting less common.

Short answer: Use "undiscoverable". It's much more common.

Long philosophical answer: Whether something is in the dictionary or not is not a great way to decide whether it's "a word". Some dictionaries are very inclusive, and include every word that someone might find, even if it's very rare or archaic. Other dictionaries are more selective and will only include more common words.

Also, English lets you add a lot of prefixes and suffixes to words, so that you can make new words from a single stem. For example, if you can rotate something, it is rotatable. If you can't rotate it, it's unrotatable. Its condition of being unrotatable is its unrotatability. It's not hard for an English speaker to understand what you mean when you say "unrotatability", but I doubt you would find it in any dictionary. I've probably never said or written it before in my entire life. So is it "a word" or not? Well, clearly you could use it as a word...but you wouldn't find it in a dictionary. And if a dictionary decided that it should include unrotatability, what about unpushability? And unshiftability? etc. A dictionary can't possibly include everything that could be a word.

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