Mixing Autokey with Regular Vignere
It can still be done, because some letters of the English alphabet are used more often. Analyzing a ciphertext based on the frequency of appearance of some characters is fittingly called Frequency analysis.

This method of cryptanalysis gets better, the more ciphertext you have. If the plaintext is in English, then you would know, that the most frequently used letter would be "e".

Because the Vigenère cipher is quite an old method of encoding something it can be (and has been) broken relatively easy by hand. The security relies on the keylength and the "randomness" of the key. 10-20 random letters is actually pretty good, but with a very long ciphertext you can ultimately still break the Vigenère method.