Your staff member has produced a pattern of absenteeism.
The correct thing to do is to make it clear to the staff that you now see a clear pattern of absenteeism and this kind of behaviour will not be tolerated as of now.

record this attitude change of the company and inform staff that in future such behaviour will receive a 2nd level warning followed by final then dismissal.

Keep to your threats , issue 2 warnings and then dismiss. the sick letter on saturdays is a cover . show the staff their records and their patterns.
If the staff all use a common Practioner then obviously something is amiss (maybe you need to give him a call)
Compile a dossier for the CCMA if it comes to that.
Your Labour consultant should be informed of the route you wish to take and ensure that all paperwork and correct procedure is employed to achieve your objective.

If you continue being soft your staff will continue to ride over you .
Its time for you to take a stand And put your foot down