Unisa used to have a limited application period but they recently changed their system.
The new application process is called 'open applications' which means that applications remain open the whole year.
There is no closing date as such. However specific qualifications may be closed for applications when a qualification is full or at least two weeks prior to the start of the registration period.
For undergraduate qualifications, honours degrees and also postgraduate diplomas you are able to apply at any time during the year.
However this is not a guarantee that you will be able to register for the next semester or even the subsequent academic year. It will depend on, among other things, whether you meet the necessary admission requirements, whether the qualification is full (over-subscribed) and whether the registration period has commenced.
It is also subject to the prescribed minimum tuition period of 15 weeks for semester modules and 30 weeks for year modules.