Upvote:2
I do not thing you get troubles, but your address may get blacklisted, and so you may not notice new appointments. I think 10 or 15 minutes would be better and less noticeable. Especially if you add also a random timeout.
I would try to avoid to get blacklisted, you may get trouble later on log-in from your computer.
Next time, try to better plan.
Upvote:3
Would I get in trouble if I refresh a webpage of a country's visa appointment website every minute 24/7?
No problem, 1 request/min is very light, nowhere near the DDoS laws. Check the website's ToS if you want to be extra careful, but I've never read such restrictions.