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But Ms Curran dismissed his comments, saying he had been "relentlessly bagging me for at least a couple of years" and she did not know why.
She suggested the primary reason Labour's vote was down in the electorate was because nearly 5000 people did not vote.
While the candidate votes for National in the seat were almost identical to those on election night in 2008, votes for Ms Curran were down by 2132, giving her an election-night majority which was 2125 lower than in 2008.
Last election, once special votes were counted, her election-night majority rose from 5992 to 6449.
In the party vote, National made gains in the electorate on Saturday night, with its proportion of the vote rising to 40.04% compared with the 34.03% final result at last election.
Labour's share of the final result last election was 46.5% compared with 34.7% on Saturday night.
Speaking about the reduction in the Labour turnout in a seat widely regarded as one of the safest for the party in the country, Dr Edwards said he expected there would be some serious unhappiness about Ms Curran's candidacy.
She would need to do something quite significant to be able to reclaim the confidence of the party in the electorate and in party headquarters, he said.
"I think there is a very good chance she won't be standing again in 2014," he said.
Ms Curran said there was no disquiet within the party about her as far as she knew and she had been talking to "a number of my colleagues".
She planned to stand again and would do everything she could to find out why people had not voted and to give people a reason to vote for her next time.
In North Dunedin, the collapse of the party vote was also evident, with only 587 votes separating National and Labour on the night, compared with 2008, when Labour was more than 4000 votes ahead.
Dr Edwards said the results in the two electorates reflected the lack of campaigning for the party vote from both Labour candidates, but he would give Dunedin North's new Labour MP David Clark a bit more "leeway" than Ms Curran on that issue since he was a first-time candidate replacing a long-serving MP who had much loyal personal support.
National's Michael Woodhouse and Joanne Hayes had done " a very good job".