Playing on a sponsor's invite, Hoey, 37, produced a third straight sub-par round at Leopard Creek.
Hoey is 11 behind leader Brandon Stone going into the final round.
The Belfastman has endured a dismal 2016 as he lost his European Tour card and then also missed out at the qualifying school in Spain.
However, five-time European Tour winner Hoey fired opening rounds of 69 and 71 and his steady three-birdie card on Saturday kept alive his hopes of recording a decent finish in South.
Heading into the final round, Hoey is three shots behind the players who share 10th spot.
First-round joint leader, Paul Dunne is alongside Hoey on six under after hitting a level-par 72 on Saturday.
Home player Stone increased his one-stroke overnight lead to three shots as he carded an impressive 66.
Stone leads on 17 under par with compatriot and tournament favourite Charl Schwartzel (68) sharing second spot with another South African Keith Horne and England's Chris Hanson.
Michael Hoey is sharing 23rd spot after three rounds at the Alfred Dunhill Championship after firing a third-round 70 in South Africa on Saturday.