After 3 Years of PhD - problems with University registration - Fight or apply for another PhD
For the benefit of the wider audience, a little background into the German PhD system is in order.


Researchers after the master's level are hired as Wissenschaftliche Mitarbeiter (researchers, literally "academic personnel"), and work for the individual research groups as half- or full-time employees, with the commensurate salary and benefits.
In parallel, students are expected to register as doctoral students (Zulassung). Such a process will typically involve some classwork for international students, particularly those studying in engineering fields (and those with degrees other than the area they're now studying). One of the forms to be filled out in this process is the Betreuungsbestätigung, which is a commitment by the signer to be the candidate's advisor. 


Normally, deadlines are deadlines; however, if there are mitigating circumstances, many departments will allow the advisor to petition for exceptions to be made. Given that you've made good research progress, it would seem reasonable that your advisor would want to ensure that you get your PhD. So, before doing anything else, talk to your advisor.