The former African champions are currently second in their qualifying group (Group E) and they only need a point from their final match with Libya to secure their spot at Africa's showpiece event.
Despite the fact that Bafana are the only unbeaten side in their group, pressure has been mounting on the British tactician ahead of the clash which will be played in Sfax, Tunisia.
The two-time Premier Soccer League (PSL) title-winning coach has acknowledged the pressure that exists.
Baxter recently opened up and stated that he would seriously consider quitting his national team coaching job if South Africa fails to qualify for the continental tournament.
This just goes to show that the former England under-19 coach is indeed feeling the heat and the weight of expectations from the fans, media and his employers, the South African Football Association (Safa).
It is surely Baxter's biggest match as Bafana coach since the 2018 Fifa World Cup qualifier against Senegal in November 2017.
South Africa's hopes of going to the global tournament ended after Senegal secured a 2-0 win over the hosts at a packed Peter Mokaba Stadium.
The former Kaizer Chiefs coach survived the axe and he was entrusted with guiding Bafana to the 2019 Afcon finals as part of the building process for Vision 2022.
It is the third time that Baxter is finding himself in a do or die situation while in charge of South Africa having resigned from the Bafana job in November 2005, after failing to qualify the team for the 2006 World Cup.
Last year, the 65-year-old decided to stay on as he had the support of the Safa leadership and this gave him the confidence to continue.
However, failure to guide Bafana to this year's Afcon could negatively affect his relationship with an organisation whose patience will certainly be tested,
A defeat to the Mediterranean Knights would also define Baxter's disappointing second Bafana stint having failed to qualify for two major tournaments.
Bafana's Afcon qualifying campaign has seen them fail to win at home to Libya and away to Seychelles, and losing to Mediterranean Knights could leave Baxter feeling that he has lost his grip on the team.
Tendering his resignation would seem like the best thing to do before facing a potentially embarrassing dismissal by Safa.
As things stand, the former Finland head coach has control over his own fate heading into this weekend's clash.
Baxter should ensure that his side is well prepared for the clash with Libya as he looks to mastermind a victory.