Well, it doesn't seem to be an issue of the site, it seems. Or is it?

- What happens in between with the router? Is it turned off or does it stay turned on?
- What happens in between with the computers? Are they turned off or do they stay on or standby or hibernate?
- During the day, what does ipconfig say about the validity of the lease.
- Why do you have to reset their IP address. Why not your friend (who works there) or the users themselves. Quite a nuisance if you have to go there every day if you don't work there.
- What program gives the message? The browser they use to access the program? An application that connects to the database?
- Why ipconfig /renew? Doesn't it suffice to reconnect from the icon in the system notification area? Or does the message come while it's still connected and all other internet connected programs (like a browser and their e-mail program) work?
- What does the IT person that is responsible for the network at the office say about it? I assume the doctor doesn't do the IT management himself, so he has it outsourced.

A very unclear and incomplete post indeed. I'd really advice the doctor to contract a professional IT and network management.