PhD position: got rejected - reapply?

Question

I applied for a PhD position and I was invited to give a talk about my Master thesis, but I didn't get the position, because:

1. Maybe my talk wasn't as good at it could be- I wasn't ready with my thesis then and I made some mistakes. I guess I could work on that.
2. My current thesis advisor probably didn't give me good references, although I'm not sure about that. There is nothing I can do about that- try to explain the disagreements I had with him to the committee? No one asked me about that, so I won't get that chance in the future. But I could ask someone else to write a reference letter for me.

My question is:

Should I apply to the institution again (in few months or 1-2 years) when they have another open position? How will it be perceived?

My main concern is that the application will be reviewed by the same people I talked to, the people who took part in my seminar. Will I be allowed to give another talk on the same topic?

Also, the person who wrote to me, didn't suggest that I apply there in the future.

I'm not going to get more experience in research, because I work in a company, but I can have some publicaitons.

Note:

1. This is not a duplicate of this question, because I didn't withdraw my application- I was rejected.
2. This is not a duplicate of this question, because I was invited to the university, I had a talk with the group members and I gave a talk there. My experience isn't a problem, its the general impression, my knowledge (?).
3. This is not a duplicate of this question - see my explanation for the second question.

Answer 1

If I were in your position, instead of submitting a 'cold' re-application, I would first contact the committee and ask them for advice about what I could do to improve my prospects of being accepted as a PhD student. I have seen people do this a few times, and the strategy receives positive responses from faculty; but of course you will then have to do the work and actually improve on the things they suggest.

Re-applying with exactly the same material will probably not get you anywhere. However, if you get advice from the committee and/or from other people who are experienced in the field about what to improve or what skills/experience to acquire, and if you can demonstrate the results well, it will be noticed.

Answer 2

It is, most likely, a waste of your time and that of everyone else as well: If they rejected you once, what do you think would make them reconsider? The reality is that they probably didn't reject you for only one reason (talk, one letter missing), but for a number of reasons. It's unlikely that bringing one more letter would make them forget about the talk, or whatever else it is that they didn't like about your application.

It is true that that may not be fair. But it's just how humans work: Once you've made your decision that someone doesn't meet your expectation, there doesn't just have to be a small amount of extra information to change the outcome. You'd have to be able to demonstrate some extraordinary progress for people to be willing to change their perception of your application.