Re-apply to a PhD position that is re-posted after being rejected? My application to a specific PhD position was rejected. I was informed about it last week and I wasn't even invited to an interview. The information was a standard email telling me that "despite your evident qualifications, there were better candidates". Now, I see that the institution re-posted a job ad for the exact same position, and only changed the starting date to a later one.

I'm a bit puzzled by this situation and don't know what to do:


Should I re-write a better motivation letter and apply again, or does the early rejection means I have no chances at all?
Should I contact the thesis supervisor and ask him what could improve my chances, like this answer to a similar situation suggests?
Or should I wait a bit, get other experiences as research staff/assistant or something similar and apply for another position later?


My biggest worry is that I might appear too "pushy" and that my future applications in this institution will be automatically rejected, even if I have more experience. On the other hand, having a feedback from the supervisor could be useful for future applications.

I am aware that similar questions have bee posted already, like this one. However, my situation is slightly different, as I would apply to the same position without any new experience (against what is advised there). The cultural setting is German-speaking Europe.
First of all, can you be sure it is exactly the same position? The same professor might have just gotten another grant which can fund another PhD position; it is then possible that they announced the second position with an (almost) identical ad. If that is the case, you can still have a chance of being accepted if you apply. If not and it's indeed the same position, it'll be much more difficult.

If it's a second position with the same professor, it means that the search for a suitable candidate starts anew. Being rejected with the previous application then isn't really a problem—it just means there was at least one candidate better than you. With a new hiring process, the selection starts from a beginning and it can happen that you'll be the best candidate this time. If, on the other hand, it's the same position, none of the candidates was a good fit for the job; and that doesn't change now unless you can change a part of your application (like your cover letter).

In my opinion, you cannot go wrong by sending a brief, polite email to the professor and asking about the new ad and potentially for a short feedback on your application. The worst that can happen is that you'll get no response at all, and then it's probably not a good idea to apply.