I don’t know of any interview/Pottermore update (yet)/other place where J.K. Rowling has commented on this, but by reviewing the speeches from the start of the 1994 tournament, we can see how unlikely another attempt was.
When Dumbledore introduces the Tournament, he notes that the latest attempt was designed to avoid student deaths:
“There have been several attempts over the centuries to reinstate the tournament,”
Dumbledore continued, “none of which has been very successful. However, our own departments of International Magical Cooperation and Magical Games and Sports have decided the time is ripe for another attempt. We have worked hard over the summer to ensure that this time, no champion will find himself or herself in mortal danger.”
— Goblet of Fire, chapter 12, The Triwizard Tournament
Cedric’s death means they failed in this regard. This alone would probably sink another attempt.
But there are other reasons why it wouldn’t run again:
A fourteen-year-old became the Fourth Champion. And won. Despite rules explicitly forbidding anybody under seventeen from competing. This severely annoyed both Beauxbatons and Durmstrang.
This would call the security around the Tournament into severe question, and likely make it politically impossible to repeat the attempt in 1999.
The two organisers are gone. We learn that Bagman and Crouch were two key players in the 1994 Tournament:
“Mr. Bagman and Mr. Crouch have worked tirelessly over the last few months on the arrangements for the Triwizard Tournament,” Dumbledore continued, “and they will be joining myself, Professor Karkaroff, and Madame Maxime on the panel that will judge the champions' efforts.”
— Goblet of Fire, chapter 16, The Goblet of Fire
By the end of the Tournament, Crouch is dead and Bagman has been discredited. I don’t think anybody’s rushing to fill their shoes.
Shakeup in the Ministry and the schools. Both Karkaroff and Dumbledore are killed in the intervening period, and the Ministry is in a period of heavy upheaval. This would make it logistically difficult to organise a large Tournament. Neither Hogwarts nor Durmstrang are really in fit shape to compete, and we don’t know what shape Beauxbatons was in.
It ushered in Voldemort’s return. Although it wasn’t recognised at the time, if the Tournament in 1994 hadn’t taken place, then Voldemort probably wouldn’t have been able to get to Harry. He might still have returned, but he wouldn’t be as strong.
I can’t see anybody falling over themselves to do the follow-up, do you?
It’s very insensitive. A Tournament in 1999 would take place in the wake of one of the largest Wizarding Wars in modern history, including a final battle which saw children and students fighting to the death. Many laid down their lives in defence of the school, and others were killed elsewhere.
Putting students in harm’s way for a sense of artificial glory or entertainment is grossly inappropriate. There are better ways to improve cohesion and cooperation in a post-Voldemort world than making sport out of children.