New Situation
Once I started testing in logging mode the problem had gone away already. There were some hints to HTTPS certificate issues, but nothing really to blame. Neither with nor without logging the problem could be reproduced after two days of questioning me.

The caching works on the base of the requested domain, that is example.org and not openpgpkey.example.org - thus it should not make a difference when you change your setup. There is an initial test for a cached domain status before the resolving process starts. If you want to look yourself: gnupg/dirmngr/server.c:cmd_wkd_get() and domainfo.c.

Reproducibility
The problem cannot be confirmed generic on domain level. I can reproduce the effect with keys shipped from my domain, i.e. email addresses @shimps.de, but the issue vanishes when I try to reproduce it with email addresses @gnupg.org as e.g. Werner's address.