Hello,
It seems that html4docx uses the HTML <u> tag to determine that text is underlined. According to this, this tag was deprecated in HTML 4 (and restored in HTML 5 with a new meaning). The "text-decoration" style property set to underline should be used instead.
HTML code example :
This <span style="text-decoration: underline;">word</span> should be underlined.
Generated docx file doesn't underline in this case.