DOCX and ODF formats are based on different principles. They have a common intersection which can describe very simple documents. But any real-case one uses features outside the common set, e.g. chapter numbering or notes. Whatever is outside this set must be approximated by the conversion process. Unfortunately when saved back and reopened, these approximations are not the same as the orginal and incur new approximations. In the end, the cumulative effect is to damage beyond repair the document.
Bibliography is one advanced feature. It is implemented with non-typographical tools. It mean it is non only text processing to format and layout characters. It involves a database and an abstract model. Very frequently, what is provided by the suite is considered rudimentary and the bibliography is delegated to some third-party extension which adds to the problem.
Also, M$ Word lags miles behind LO Writer when it comes to structure semantically your text. Word is very poor regarding styles, with the consequence that everything beyond a paragraph is done through explicit individual formatting instead of referencing a style. This makes very difficult to guess the intended structure and is responsible for the conversion approximations.
I understand your worry about your documentation asset. But trying to manage .docx documents with Writer is doomed to cause you trouble in the long run. If you intend to drop Word, convert your documents to .odt first time you edit them. This may seem a hassle but it pays off, avoiding future problems. You nevertheless keep the possibility to export DOCX if your recipients think they can’t open ODF in Word (this is wrong, but M$ also implemented ODF in a “personal” way to keep their customers captive). Always work native in any application.
The conversion process is not easy if you want it perfect. It requires pasting your text as unformatted and recreating the formatting. So, do it only on the documents you know you’ll review a lot.
There are many differences between Word and Writer. Start by reading the Writer Guide, specially the chapter about styles. Styles are in the heart of Writer processing. They are omnipresent, contrary to Word. Avoid direct formatting as much as you can (even for bold or italic) if you want versatility, stability, reliability and power in your document. Styles allow to separate contents from appearance which you can’t do in Word and which direct formatting also prevents.
That said, I can’t tell what’s happening without a small sample file.