Mr Craig confirmed that his party was taking "disciplinary action" against board member Larry Baldock, but said he did not expect it to result in expulsion.
The Conservative leader said he had also learned of "murmurings" about a leadership challenge, but he did not know where they came from.
"There are a lot of rumours around the traps," he said.
The party voted on all positions every year and no one had raised the matter of a new leader at a board meeting on Saturday.
Former Napier candidate Garth McVicar was invited to the meeting by a board member, despite resigning from the party after the election.
Mr McVicar - who returned to his job at the Sensible Sentencing Trust in October - said he turned down the invitation and he had no plans to challenge for the leadership.
Mr Craig said he did not know Mr McVicar had been invited to the board meeting but he presumed it was to give advice on future strategy.
"His input to the party would still be welcome," he said.
Mr Craig said he could not reveal why action was taken against Mr Baldock until the disciplinary process was completed.
Mr Baldock said he had been removed from the party's board and had his membership suspended before Christmas but he would not reveal the reason.
"I'm in a process of a dispute of that decision by the board," he said.
Asked whether he felt the party was in good health, he said: "No comment."
The former United Future MP withdrew his nomination for the Tauranga candidacy in opposition to Conservatives' "one law for all" policy, which included abolishing Maori seats and the Waitangi Tribunal.
He said his suspension was not related to this disagreement.
Mr Baldock was also referred to the Electoral Commission for filing false electoral returns in 2011.
Mr Craig said at the time that if police found any wrong-doing by a Conservative candidate that person would not be able to stand for the party again.
Since the election, chief executive Christine Rankin has stood down but remained on the board and Mr McVicar and board member Leighton Baker have resigned.
Mr Craig said it was common to have some turnover after an election.
- By Isaac Davison of the New Zealand Herald
