I currently have OpenVPN setup with 2 private DNS servers which are pushed to clients automatically using the options below in the server config file:

push "dhcp-option DNS xxx.xxx.xxx.xxx"
push "dhcp-option DNS xxx.xxx.xxx.xxx"

My intention is to use the 2 DNS servers as redundant DNS servers so that when one is down, OpenVPN can automatically use the other. However, it appears that my OpenVPN setup do not automatically switch back to the active DNS server if one is down.

How can I correct this and make sure that OpenVPN can automatically switch between the DNS servers?

Thanks

that's not up to OpenVPN , it's OS specific. If the tap-win32 adapter (I assume your client is running Windows) shows both DNS servers then OpenVPN is configured correctly. The fact that the OS does not automagically fail over is something else.