big-ip configuration GUI utility not loading

There are numerous reasons why this might be happening. Keep in mind that the GUI is low man on the list when it comes time to hand out system resources, and it may simply be that your unit is too busy handling to traffic to handle your login request. You might be able to improve responsiveness by upgrading to 11.6.0 or above (we change how we allocate resources). Alternately you may need to either remove some of the load on the box or you may have an actual problem. In any case, opening a case with F5 support would be your surest path to resolution. top will give you a view of your system's general load, and ihealth will help you look at your BigIP's overall health. We have logs (/var/log/httpd/), also, but they are often less than immensely helpful.