After losing 1–9 to Tony Meo in qualifying for the 1980 World Championship, van Rensberg next played a competitive match in the 1984 edition of the tournament.

The 1985 World Championship saw van Rensberg himself fall victim to a comeback, as the Canadian Marcel Gauvreau recovered from 0–3 and 6–9 to defeat him 10–9.

Van Rensberg was able to enter six tournaments in the 1985/1986 season, and recorded his first last-32 finish at the 1986 Classic, where he beat Wayne Jones 5–4 and John Parrott 5–3 before Steve Davis ended his run with a 1–5 loss.

Ranked 59th, a career-best, for 1986/1987, van Rensberg registered three last-64 finishes therein; at the International Open, he lost 3–5 to Barry West, while Francisco beat him 5–4 in the 1987 Classic and his World Championship qualifying attempt culminated in a 0–10 whitewash by Tony Jones.

A 1–5 loss to Tony Wilson of the Isle of Man, in the 1990 British Open, would be van Rensberg's final at competitive level; he never played again, and was relegated from the tour in 1991, aged 59.