F5 access in safari browse

I'm not sure about LTM, but Safari is officially supported for APM. And yes, sometimes Safari can't connect. It's rare issue, mostly happens after reboot or sleep, and the reason is unclear (looks like Safari makes some request 'improvements', and BIG-IP doesn't respond on improper request). Some workarounds that can help: switch network interface (connect via Wi-Fi instead of Ethernet and vice versa); disable Apple Firewall; reset Safari; connect using other browser, and the try Safari again; wait for some time. And the easiest way is just use Firefox, I haven't notice this issue with the Firefox browser.