Storing AES encrypted RSA private keys on a server I'm thinking about creating an encrypted messaging web application where users create RSA key pairs, they store the public key on the server for others to see and also store an AES encrypted private key on the server. Thus, to verify their identity, they can decrypt the private key and send a signature.

That said, I'm curious is this is a reasonable idea. I know some similar services that require you always use the same device (like an iPhone) and won't let you use the same account on a different machine. This leads me to believe that they are storing a private key locally on the device. It seems reasonable to me to store an AES encrypted RSA private key on the server, but I am no expert on the subject and since I don't see anyone else doing it, I'm a little skeptical.

Any thoughts or concerns about this?
Given that you used a strong password to derive the AES encryption key: Yes you could securely store your RSA private key in encrypted form on a server. BUT, since there is no technical need to have your private key on the server, why would you risk it?

Look at it that way: Suppose you have very sensible data (like private photos or so). Now you could encrypt it with a strong algorithm and password and send it to all your friends, knowing that no one would be able to to decrypt it. Anyways, I personally would still not do that. Even if I trust the encryption, I would not unnecessarily give encrypted data to someone else for no good reason.