Don't worry, it's not you or your browser.
The furthest ahead you can book is three months - as it stands, all appointment slots appear to be full. Not just for Mugla but other areas.
Try accessing it just after midnight, Turkish time, to see if the very last slot is available (16th December). If it is, great, if not then it suggests they've gone into meltdown mode due to (I suspect) the high number of foreigners wanting processed.
JF