“I can’t access your Webmail, but can browse other websites…”
Apparently, customers convince such test confirm that the said Webmail is down! But, this is not always true.
It depends on the location of web servers that host the website. Your ISPs connect you to the outside world using different networks. Problem can occur to just local or international connection.
That means, if the said Webmail is hosted in overseas while customers are browsing a locally hosted website, this will create an assumption that the Webmail is down!
Solution, email servers hosted with geographically-dispersed network in both your country and overseas!