"There is still an ongoing political battle and it is not completely won."
Ms Bradford is one of six speakers at the seminar, which is focused on moving on from the repealing of section 59.
Child discipline, parenting and the effects of last year's law change are some of the topics being discussed and Ms Bradford spoke about the political environment one year on.
Polls showed the law change was a major election issue for about 5% of voters, Ms Bradford said.
The "most powerful forces" working against the law change were those involved in the petition for a referendum on the issue.
There was no question the petition had been "amazingly successful" given that it was very difficult to meet the required 10% target, she said.
"They have poured a huge amount of time and money into it."
More signatures were collected for the petition after the first petition fell short when more than 5000 signatures were declared invalid.
A report on the validity of those further signatures was expected at the end of August.
If a referendum was held, it seemed unlikely it would be held at the next election and was likely to be carried out by a postal vote next year, she said.
"I feel sure some of the people who signed it then have changed their mind since, but that doesn't negate the legality of those signatures."
Any potential threat to the law change would depend on the make-up of the next government.
Her biggest concern would be any attempt to change the law to define an acceptable level and nature of violence, as that would send the message violence against children was acceptable, she said.
The role of academics and researchers in any future debate would be "incredibly important".
There was no evidence people were being "dragged off to court" for minor offences and she welcomed research presented at the seminar which showed 44% of voters were in favour of the new legislation, she said.
"While Family First are creating the perception 80% are against it, I feel this is much more in line and that the proportion is about 50-50."
The Children's Issues Centre is a multidisciplinary research centre based at the university.
The seminar continues today and Associate Prof Joan Durrant, a children's clinical psychologist from the University of Manitoba in Canada, will talk about the reform of section 59 in an international context.
