It would be helpful if the CA (or reseller) confirmed (dispay a warning) that you really want to reissue with the same private key and explain the implications of doing so.
When reissuing a certificate the default behaviour should be to revoke the old one after some specified time has elapsed - that is what reissuing is for and what distinguishes it from simply buying a new certificate.
The problem is that many people in the industry doesn't really understand the basics. How come is there a leak of your certificate, if that's the public key you're showing to every single client that connects to your SSL enabled site?
I've even seen sysads advising on forums about reissuing certs after Heartbleed, but no word about the keys.