What it means
ないとも限らない expresses that the possibility of the preceding negative proposition cannot be ruled out. It often conveys an unexpected or contrary possibility, such as saying that something might not happen even when it seems likely to happen. The construction is more cautious than a direct assertion and does not mean that the negative outcome is especially likely.
Usage note
The polite counterpart is ないとも限りません. With nouns and na-adjectives, use ではないとも限らない. Do not confuse this construction with ないわけではない, which primarily gives a partial affirmation or says that something is not entirely the case.
How to use it
彼が犯人ではないとも限りません。
He might not be the culprit.
この方法が有効ではないとも限りません。
This method might not be effective.
その判断が正しくないとも限りません。
That judgment might not be correct.
この薬を飲んでも、症状が改善しないとも限りません。
Even if one takes this medicine, the symptoms might not improve.
彼が犯人ではないとも限らない。
He might not be the culprit.
この方法が有効ではないとも限らない。
This method might not be effective.
その判断が正しくないとも限らない。
That judgment might not be correct.
この薬を飲んでも、症状が改善しないとも限らない。
Even if one takes this medicine, the symptoms might not improve.