After using org-save-outline-visibility the invisible parts of the buffer become invisible to isearch. I have to do something like calling org-global-cycle to restore the buffer to its original state and allow searching in its invisible parts again.
The problem seems to be in the functions org-outline-overlay-data and org-set-outline-overlay-data. They save and restore just `invisible' overlays. They should do the same with `isearch-open-invisible' overlays. Or perhaps org-set-outline-overlay-data could simply use outline-flag-region? What do you think?