It's recognised the New Zealanders face a huge challenge each year; facing hardened professionals in the top 50 or 100, after spending most of the year battling in the lower reaches at Challenger or Futures level.
"It's the consistency that shows up," says former New Zealand professional GD Jones. "Mike Venus serves as hard as [World No 16] Kevin Anderson, there's no issue there. The difference is the consistency, the concentration, the execution over time.
"These top guys are on you every point and it's mentally very tough ... your attention to detail on every shot and every point is that much higher and it takes a lot out of you."
Often the Kiwis lift way beyond the respective rankings - but just not far enough. In 2005 Nielsen, then ranked 617, pushed Italian Potito Starace (73) to 4-6 4-6.
Three years later King-Turner (344) was a few points away from beating world No 20 Juan Ignacio Chela before going down 7-5 2-6 5-7 and in 2009 King-Turner lost 4-6 5-7 to eventual finalist Sam Querrey.
Venus also had a brush with glory in 2011, taking the first set off former World No 5 Tommy Robredo before succumbing 7-6 (6) 3-6 0-6.
These performances have been solid, though other occasions have been more one-sided. It led to some questioning whether it is good for the image of the sport here - to see Kiwis struggling at the showpiece event.
"I don't think New Zealanders understand the global nature of tennis," says Heineken Open tournament director Karl Budge. "It's the second biggest sport on the planet and incredibly competitive. Generally the Kiwis here are competing quite well."
Jones offers a unique perspective on the issue. A former ATP professional, Jones also coached Kevin Anderson into the top 20.
He had contrasting experiences in his two Auckland appearances (2005 and 2008).
"The first time I was so nervous," says Jones. "I hit my foot with my first serve of the match. I was so overawed by the occasion and lost 0-6 2-6.
"The second time I won through qualifying and it was very different," adds Jones. "I'd practised with some of these big guys, I'd won a couple of matches and I felt like I belonged here, that I deserved to be out on the court. That is the key, having the inner belief that this is where you are supposed to be. We saw that [yesterday] with Wesley [Whitehouse] and Finn [Tearney] who weren't overawed by the occasion at all. If you have that inner confidence then you will put your best foot forward."
Jones has no doubt that Kiwis belong in the event, even if the results have been disappointing over the past decade.
"It's great for the tournament - people want to see New Zealanders on court and up against some of the best guys in the world."
