There is a big issue in Atahualpa 3.7.9. Atahualpa saves options on frontend. Thus, at first visit in a translated language, the options are saved in the translated language and translations (which are done in only one direction) are broken.
It seems to occur only when using the function 'bfa_widget_area'. A quick workaround is to comment the line 479 in functions.php
update_option('bfa_ata4', $bfa_ata);I don't know how much it impacts the theme.
Here is another possible solution which does not modify the theme (possible with 2 languages but difficult to manage with more than 2).
Polylang does keep all the translations while the checkbox "Clean strings translation database" is kept unchecked. It is then possible to save all the options in the first language and translate them. Then resave all the options in the second language and translate them. Although it won't be "visible", the translation will work in both directions while keeping "Clean strings translation database" unchecked.
The best solution would be a modification of the theme which must not update the option which contains translatable strings on frontend as it most probably break all multilingual plugins.