Connectivity issue is a very common definition and may encompass many problems.
However, in our case the most common definition is: unexpected network failure at one of our upstream network providers that affects the connectivity to your host server.
We use multiple Tier 1 telecom providers; thus bypassing transit networks which shortens the network path between your website and your visitors.
However, this also means that when your ISP or its upstream providers experience connectivity problems, you or some of your visitors who pass through the problem providers would not be able to access your website.
All other visitors will be able to visit your website without any problems.