I have been working for the same company over almost 10 years now, always on temporary contracts, although I am a staff member (not a contractor). It seems that they are now also keen in offering me a promotion, but again under a limited term contract. I am interested in taking that position, if they would offer me an unlimited contract instead. Could you please share sound argumentation to successfully negotiate this with the HR department?
If you are working in Germany, and at the same company for ten years, then German law puts facts ahead of contracts. In this case, the FACT that you worked there for ten years would override the CONTRACT that says your employment is for say one year only. You cannot use contracts to change facts in Germany. In practice this means that your notice period and your severance pay will be the same as for everyone working at a place for almost ten years.
There's no need to press for a new contract. Actually, a new changed contract could be legally to your disadvantage since you intentionally deviate from the current facts.