Lokking for Email Catching Provider

Hi,
Our company’s ISP is cbeyond, we host our own email server on site thus our MX records is pointing to our server. in our location we have experiece a lot of power outage. once that happens and UPS are low….all servers are shut down. therefore all emails will be rejected until power is restored.
I want to know if there is a provider out there that will catch incoming email and store it untill our email server comes back than release all emails to our server. WITHOUT switching ISP.

Thanks