It's a bit anecdotal, but after encountering this same problem, I did some trouble-shooting and believe it *may* have been introduced with one of the recent updates to the FreeNAS 9.3 trains (I subscribe to the "STABLE" train). After installing an update at the beginning of April, I found the console log would not pop-up from the web GUI footer any longer (just displays "Loading....", along with the "Stop Refresh" checkbox). I use Firefox (latest version), and normally when I encounter such problems, a refresh of the FreeNAS page/tab will get the console log pop-up going again. But, that was not true after the update was applied - I also tried some things suggested in other FreeNAS / Linux posts (restarting the console log service, etc) without luck.
It was when, after trying a reboot of the FreeNAS still didn't resolve the problem, I reverted back to the prior boot environment (201503270027) and that restored functionality of the console log pop-up. I haven't had any issues since then (it's been a few weeks). I find the scrollable pop-up feature very convenient and valuable....it helped recently in trouble-shooting a failing hard drive that wasn't initially evident from the S.M.A.R.T. output, and is easier to quickly navigate compared to shell commands with the MORE pipe (or redirecting output to a file).