Wifi issues with DHCP at work.

When a device connects to a network via DHCP, it will usually ask for the same IP address it had previously, which your DHCP server is free to honor or not.

With most hotel routers, an IP address is assigned but the device is not allowed through the firewall until the first DNS request occurs, which causes a redirect to the hotel's Terms of Use page.

You may want to investigate how your DHCP servers are configured and, when you have no connection, if when you enter the name of a site you had not previously been to (something like ibm.com) the DNS activity causes a redirect to your property's ToU page.

Those are the Cloudflare DNS servers, so I suspect you are good there.

It still sounds as if when a device requests a previous IP address and is granted it, something in your router is not allowing access as opposed to when a new device requests a new address. Some routers have firewalls that are explicitly set up to work just that way.

You would have to check the logs on your router/DHCP server to troubleshoot that further, or ask your IT staff if you have one.

Can you access any sites at all when this happens, or do sites just all time out?

Yes, multiple DHCP servers active on the same network can wreak havoc.

Have you tried Resetting Network Settings? This will remove all WiFi & Bluetooth configuration profiles to allow you to start fresh.