SSL renegotiation is a function of the SSL/TLS protocol to renegotiate the session, usually to refresh the keys, but is also used in "step-up auth" scenarios. SSL persistence is a mechanism employed by a load balancing device to ensure traffic from a single session persists to the same backend server, based on the SSL session ID. Keep in mind however that modern web browsers and web servers will renegotiate the TLS session often, making SSL persistence generally unreliable.
10 SSL SSL handshakes in 10 minutes doesn't seem like an unusual traffic flow. Is this not web traffic?
Again, depending on the application protocol, it's not unreasonable for a client and server to re-handshake every so often.
Are you looking at dozens of SSL handshakes or thousands/millions? HTTP is a stateless protocol, so browsers can and will renegotiate SSL sessions reasonably often. Hopefully you'd see more resumptions than renegotiations from a single client, but it generally depends on the client.