analog zu Kernkompetenz

core = (literal,figurative) Kern/Inneres/durch und durch ~subject (school)= Hauptfach/Pflichtfach

See the links below for examples of the applied usage of this term.
Hope this helps!

Because I have never heard the expression "Kernkundschaft," I looked
up the term in several books i.e.
Duden etc. and could not find it.
What I found, however, is that Kern
means also Haupt-, wesentlich, wichtigster Teil einer Gruppe etc. in Verbindungen (Muret-Sanders, Duden),
therefore I would suggest the translation "Hauptkundschaft" oder
auch "Stammkundschaft." Oder auch:
Der wesentliche Teil der Kunden, der
Hauptbestandteil der Kund(en)schaft.

"Core customer" is not even too widely used in English either, only about 1000 Alta Vista hits. "Core customer" was not mentioned in NODE, but NODE defines "core" as "an important unchanging group of people forming the central part of a larger group". The word "unchanging" is the reason why "core" is not so often used with "customer" as with "business" or "activity". Even important customers change suppliers.

"Kernkunde" yielded only 1 Alta Vista hit and "Kernkundschaft" only 9. It was not in any of my 5 BWL dictionaries, Langenscheid MS, Duden or Pons.

"Stammkunde" has the opposite problem. Over 1000 hits. Here though the customer(s) has/have been with us for a long time but may not be big (read important).

"Hauptkundschaft" had only 29 hits. "Hauptkunde", however, came up with 144 but most of them meaning only one customer or one customer type. Mostly used to speak of the danger for a supplier in having too few customers. Not positive.

DaimlerChrysler often mention "sticking to their core business: cars" meaning their traditional business. - "traditionell* Kunde oder Kundschaft".

These ideas didn't get many hits either but I think they would be my choice because I do not like any of the other German possibilities, nor "core customer" in English either for that matter.

- HTH - Dan