E-mail deliverability analysis & recommendations

I am facing a challenge where some of the transactional e-mails sent by a cloud-based platform I developed are not reaching their recipients, even at customers where our domain is white-listed.
Some emails are not received at all but are actually sent by our platform, while we receive no delivery errors.

We need expertise to analyse what's wrong and what we should do to make our transactional emails reach their target.