I have been working with National Fishery Authority, Papua New Guinea for almost 6 years now. Started in 2012, signing a 1 year contract which ended in 2013. From 2013 to 2014, I worked for 2 years without a contract. In 2015 January, I signed a 6 monthscontract with the confirmation from organization that we should be made permanent workers before this 6 month contract ends. However, since the contract ended in June 2015, I am still working as a casual worker for this organization to the current date. I am a marine biologist working as research assistant since 2012.
Yes, an employer can do that, it's not very ethical, but in PNG you don't have a lot of recourse I would think. There may be legal implications, but we don't give legal advice here so I'm answering in practical terms.
Basically an employer can do whatever they want, it's up to the employees to vote with their feet or fight them with a lawyer. But so long as employees allow them to get away with it it's a fait accompli as you have seen for a couple of years.
If you don't believe their promises, then demand a contract, be prepared to back up your demand with action bearing in mind that marine biology research assistants are not that difficult to replace in the Pacific.