I always cancel immediately when I get a BC "BahnCard" (same day or week), these days usually the trial 25% version (3 months, automatic 1 year subscription if you don't cancel).

It used to be pretty bad but nowadays you can cancel a BahnCard online, I used that service at least three times already during the last two years:

https://fahrkarten.bahn.de/privatkunde/kontakt/kontakt_start... (Choose as subject "Kündigung Ihrer BahnCard [25|50]" - page is English, options text still is German)