Hi Mohit, not sure we can renew it without downtime. But we can renew it with a blip of few seconds when we have the new certificate and key are ready on the LTM. And for persistence connection, YES !! the session need to be re-initiated.
As per as my undestanding, there will be no downtime for renewing the certs on LTM . Existing connections will use the old cert/key (about to expire). once reloaded with the new cert and key the new sessions will start using the newly installed cert.