The Fixed Term Work Act does provide that any employment started after 14 June 2003 can be governed by fixed term contracts for up to 4 years.
This is not ideal but generally most discussion around this act now suggests that contracts should be related to purpose more so than time.
Does your partner's contract mention a specific reason for their employment? She is entitled to this reason by law.
As to when a person can be made permanent, it is really up to the employer. As far as the Fixed Term Work Act is concerned, if your partner was to be employed on contract for longer than four years continuous service, they are entitled then to a contract of indefinite duration i.e a contract with no expiry which can often mean permanency.
Obviously she cannot be terminated by virtue of coming near the four-year mark either or, under the Act, she is entitled to an indefinite contract also.