Do you send multiple emails from the same sender?
If yes, what is set for "Days between responses"?

Several mails are sent one after the other with a pause of at least one minute. The "Days between responses" is set to 1.
However, I assume that this delay time should not have any influence, as every mail should be answered if the option "Always send vacation message response" is activated.

VacationConf.jpg (164,505 bytes)   

VacationConf.jpg (164,505 bytes)   

Wrong assumption :-)
This option always aplies.

"Always send vacation message response" only changes the sorting of sending vacation messages and filters.
If not set, filters will come first.
If set, vacation messages are send first.
That is all.

It is confusing for me: What is the correct setting so that every mail is received and further more an out-of-office message is sent on every single one of these received mails?

Sorry, but as of https://datatracker.ietf.org/doc/html/rfc5230#section-4.1 this is not possible.
It states, that the minimum value between auto replies has to be 1 day.

I personally don't see a use case for having an auto reply for every email.
If the sender ignores your first, why send another?

Personally, I understand your point of view. But for my boss and also for some customers it is a "must have" feature. At the moment we are working with ISP configuration and webmail and the users are familiar with the auto-play of each email.
If we could configure "days between replies" with 0, wouldn't that fix this problem?

Obviously I wasn't clear ;-)

Vacation auto replies are implemented via SIEVE rule.
SOGo only is a frontend, setting that SIEVE rule.
SIEVE is implemented in your IMAP server, either natively or via plugin.
Every standard compliant SIEVE implementation will not allow setting "days between replies" to 0.
You would need to reprogram that SIEVE implementation, in order to allow SOGo to set it that way.
And both would break the standard doing so.

Thank you for your well-founded answer - I am now trying to make the users understand the advantage of the "days between response".