Like you say "the odd reboot of the router" which would fix a stale / corrupt cached DNS entry for the site.
If the site has moved to a new IP address then whilst they would have changed thir DNS records, if the TTL is 12-14 hours (fairly standard) then any DNS server, be it the one in your router or any caching resolver (DNS server) upstream of there would report the old address until the TTL expires if it's already in its cache.
If the DNS record was unavaialble for some reason then your device, possible your router and possibly other upstream DNS servers may "negatively cache" the lack ofDNS response for a period of time.
In short, there are lots potential reasons for the problem!
As you haven't changed nothing in the router, perhaps you can state what it is that you have changed?