connectivity

Right now, there is some Live issue. In general, a good local connection doesn't guarantee a good connection to the Live server, and loading other sites, which are hosted in different locations, doesn't tell you much. The problem could be client side, or at any hop along the path.
In this case, it seems to be widespread and impacting Live.

Do you think the problem will disappear if you start paying for a membership?
The only difference will be you won't get ads. That may improve the connection some, but may not be a major change. If there are issues between you and the site servers, that membership level won't impact things much.