In 2006, White narrowly escaped the sack after a 49-0 drubbing in Australia and one year later guided the Springboks to victory over England in the Rugby World Cup final.
White lost seven Tests during the pre-World Cup season and Coetzee suffered a record eight defeats this year in 12 internationals.
Touring Europe this month, South Africa were beaten 37-21 by England, 20-18 by Italy and 27-13 by Wales.
"Every coach goes through a rough year," the 53-year-old former Stormers Super Rugby handler told reporters at Johannesburg airport.
"I would rather take the defeats at the beginning of my tenure than experience a slump during the third year. Results can only get better from here."
South Africa were humiliated 57-15 in Durban last month by New Zealand, a record winning margin between the arch rugby rivals.
This year, the Springboks fell to Italy for the first time, lost at home to Ireland for the first time and were defeated in Argentina for the first time.
Recently appointed South Africa Rugby president Mark Alexander says Coetzee will be interviewed during December before a decision regarding his future is made.
The former scrum-half signed a four-year contract as successor to Heyneke Meyer last April, taking him up to the 2019 Rugby World Cup in Japan.
But many Springbok supporters have vented their anger on social media at the losing streak and believe Coetzee is out of his depth as a Test coach.
Coetzee defended his choice of hooker Adriaan Strauss as captain, hailing his "leadership under fire.
"He steered this team on and off the field in a tough situation and that shows his leadership ability," said the coach.
Strauss retired from Test rugby last Saturday after the defeat by Wales in Cardiff - the seventh loss for the Springboks in eight internationals.
"I knew it was going to be a tough year, but it proved much harder than anticipated," admitted the former skipper. "I gave it my all and did everything I could."
South Africa return to action next June with a three-Test home series against France.
Original source: Results can only get better from here - Coetzee