Disciplinary proceedings were launched against Mr Akker after members found he had attended a meeting with other union leaders and Labour party representatives to discuss how the unions might support the party in the run-up to the next general election.
Members feared that, since NATFHE is not affiliated to Labour, the meeting - held at the union's head office - could leave the union open to court action for misuse of its funds. That could have led to funds being seized.
Following the disciplinary hearing, the general secretary had his work regularly monitored by a panel of officials.
The action has shaken Mr Akker's status as leader of NATFHE. One national executive member called for his resignation, saying: "There is general consensus within the national executive committee that the continued employment of John Akker as general secretary is detrimental to the interest of the union."
Mr Akker, who is 18 months into his five-year term, leads a traditionally volatile union which has already voted out two general secretaries in the past seven years for misjudgments.
Geoff Woolf misread members' attitudes over the protracted contracts dispute. He came in from the Left, pushing out Peter Dawson, a victim of Thatcherite legislation on ballots for general secretaries.
Since the disciplinary action, Mr Akker has suffered a further blow after the NEC unanimously carried a motion calling for his explanation for failing to carry out task was "unsatisfactory".
The NEC found he had delayed sending NATFHE's proposals on joint membership to rival union the Association of University Teachers. That meant the AUT were able to publish its proposals first, wrong-footing NATFHE.
Mr Akker is understood to have told the committee a high workload had prevented him meeting the deadline for the proposals.
Mr Akker declined to comment.