Were there any changes to your network provider when you got the new Cisco?
There is no good reason from the LE side that a test from the Staging system would reach you but production would not. Sure, they are different IP addresses but the primary validation servers are in the same locale / system. They use one of the Cloudflare commercial networks (Magic Transit?) for the primary center and AWS based for the (currently) 4 secondary centers. Yours is failing at the primary as otherwise we'd see "Secondary" in the error.
Do you see the inbound HTTP request reach your Cisco? If not then somewhere in the backbone the packet is getting lost. These sometimes resolve on their own as the network providers discover and repair the problem.
Yes, switch to using the dns-01 challenge. Looks like GoDaddy is your DNS provider and they recently re-opened their API for this purpose. Beyond that I gave this advice which may be an option for you too: Posh-acme db_error submitting renewal - #8 by MikeMcQ