If a PhD position I applied for and didn't hear back from is removed and relisted, does this mean I was rejected? I just wanted to know your opinion about an issue. I have contacted the supervisor of a research project for doctoral student position and I was encouraged to apply. By the way my experience really fits the position.

I applied through the online application platform and after that I didn't receive any mail regarding my status. Then the post for this research position was removed last week and I just saw that the position post is online again. 
I think that they are not interested in me, because if they did I think they would have contacted me and not put the post again to search for applicants.
What do you think? Am I rejected?
Reposting a search does not mean that all the applications received so far are unsuitable. It often means that they have not received the volume of applications they expected/wanted and are worried, without having necessarily looked at the applications, that they might have missed qualified applicants.

Given you applied on line and never got a status update, it is always reasonable to ask if everything is okay. Given the position has been reposted, it is worth asking if you need to resubmit your application. Sometimes HR and electronic systems do not carry applications over from one position to the next.