There are a few things that could lead to what you're describing. The most common, is that the page is timing out. If you stay on the 'add contacts' page for too long, sometimes it will time out, and for security reasons you'll be unable to continue. There are also some security programs which might be interfering with our connection, and preventing additions to that secure page.
For both of those problems, simply adding the contacts 10 at a time, should resolve the problem. If you have a larger list, it may be easier to instead put the contacts into an excel or CSV file, and then upload the file all at once, rather than group by group.