μένω is a typical liquid verb (look up "liquid aorist" or "liquid future" in the index). As such, it takes liquid future, aorist and sometimes perfect forms. Mounce, in Basics of Biblical Greek, discusses these verbs (§23.12, p. 201 in the first edition).
Liquid verbs are those whose stems end with a liquid consonant. These consonants are λ, μ, ν, and ρ. They are called "liquids" because when vocalizing them, air flows around the tongue (λ and ρ) or through the nose (μ and ν). The presence of the liquid consonant at the end of the stem makes it difficult to pronounce the -σ- of the tense formatives of the future and aorist cases. For these verbs, -εσ- is used as the tense formative for the future tense and -α- is used for the aorist (probably was -σα- but the σ drops out under the influence of the liquid preceding it).
So for μένω, the future case is built as follows. Suppose you wanted the future active indicative 1st person plural. It is constructed out of the stem + tense formative + connecting vowel + primary active personal ending:
μεν + εσ + ο + μεν --> intervocalic sigma drops out --> μενεομεν --> contraction of the vowels --> μενοῦμεν.
Similarly, aorists are formed from the augment + stem + tense formative + secondary active personal ending. The aorist active indicative 1st person plural is thus:
ε + μεν + (σ)α + μεν --> compensatory lengthening (for the lost sigma of the tense formative) --> ἐμείναμεν
So, that's liquid futures and liquid aorists in a nutshell. Hope this was helpful.