
The Belgian top seed beat Italian Francesca Schiavone for the seventh time without a loss 7-5, 6-4.
But the further she progresses in the first major of the season, the more Henin said she knows the end of the record could invariably arrive.
"One day or another, I will lose - that's the game," the 25-year-old said. "I hope it's going to be as late as possible."
Henin last tasted a loss at Wimbledon, beaten in the semi-finals by Marion Bartoli. Since then, she has won six titles and has moved into the fourth round in Melbourne.
"I've been so consistent, but every match is different," she said. "You have to start again all the time. If you're not in your best level, you know you can lose. Every time I wake up now, I know I can win - I know I can lose.
"... I hope it's not going to be for this tournament."
Henin had to work to get past Schiavone in a combative opening set before settling into the second. "I was glad to win in two sets," the seven-time Grand Slam champion said.
"She's always given me a lot of trouble in the past," she added. "It was a tough third round for me, and I'm glad to go through."
The 2004 champion advanced in one hour, 41 minutes as she is playing the tournament for the first time since quitting the 2006 final with stomach pains against Amelie Mauresmo.
Henin overcame 27 unforced errors, breaking on five of seven occasions while losing her own serve three times.
Czech 12th seed Nicole Vaidisova finished with a screaming down-the-line winner on match point to put out Japan's Ai Sugiyama 6-3, 6-4.
"I was a little shaky, a little nervous," Vaidisova said. "I really wanted to do well and play well, but she's a very steady player and made a lot of opportunities for herself."
Russian men routed opposition in straight sets with number four Nikolay Davydenko hammering Frenchman Marc Gicquel 6-3, 6-2, 6-3 and 14th seed Mikhail Youzhny overcoming the serve of Croatian Ivo Karlovic 6-2, 6-4, 6-2.
By Bill Scott, dpa