OK, I've figured it out eventually.
In case it could help somebody later :
I have updated the *styles/forum_7582/template/ucp_register.html* file : the section following the line with <!-- END profile_fields -->
was not the same than the one in the subsilver theme. I replaced it with the the subsilver code for the said section :
<!-- IF CAPTCHA_TEMPLATE -->
<!-- INCLUDE {CAPTCHA_TEMPLATE} -->
Cleaned caches.
The Q&A shows at least, and works fine.