Yes, your analysis is right. Don't know why Maarten Bodewes - owlstead says something else. This doesn't mean that your scheme is secure or the best idea.
Every plaintext block will be encrypted with a new, pseudo random key. If the bit generation of the stream cipher is secure then there's no known way to get the original password without brute forcing it.
All in all you just use a stream cipher, but not with the common XOR operation to combine the key and the plaintext, but with a block cipher. You will still have all the security properties of a stream cipher, at least if the block cipher is still "secure". Even if the block cipher is broken it's still very hard to break the encrypted block because there's only one block encrypted with the particular key.
But what happens if the key generation is broken? The attacker has to have known plaintext blocks and the appropiate ciphertext blocks. With a secure block cipher, it's still only possible with brute force to get the key - and then he or she only has one part of the key stream of the stream cipher. (This only holds for "normal" breaks. If the stream cipher starts to output the same known key for every block, then all hope is lost.)
What happens if you reuse the key? Every identical plaintext block at the same position (index of the block position) will be encrypted to the same ciphertext. If the plaintext block itself or the position in the whole plaintext changes, then the output block will change completely (because of the avalanche effect of the block cipher). Changing the position of the block changes the key used to encrypt the block, and there's no (assailable) correlation in the output of two instances (with different keys) of a (secure) block cipher, regardless of the used plaintext. If only the plaintext itself changes by one bit, then you will still have no (assailable) correlation. The use of a block cipher defies this attacks on the whole cipher, even if the same original key was used.
Timing or power attacks could be a problem for this scheme. You do the key setup of the block cipher not only one time (like in a normal block cipher mode), but as often as the amount of plaintext blocks. Attacks on this have much higher hopes for a success.
But be warned, you still have some problems of the typical stream cipher. For example the same plaintext encrypted with the same key will still lead to the same output. Your scheme doesn't change this, and you still need to use different keys every time you want to encrypt a message - the same way you have to do it for a normal stream cipher. Changing one bit of the output message will destroy the whole plaintext block. It's still advisable to just use a normal encryption mode with a block cipher - as the other answers already mention, it's still faster, esier and maybe more secure to do this than inventing your own scheme.