I highlight text, right click. Select character and put a border around text. Later the border is missing, especially when reopening document to keep working on it.
Did you make the character border a style?
Have you saved your document in native .odt format or in a foreign format that might not support character borders?
I was saving the document in .docx rather than .odt Maybe that is the reason?
Indeed, better work in native ODF, see here why: [Tutorial] Differences between Microsoft and AOO/LO files.
Create a character style with the border.
Just put your border around as usual, then while the characters are still selected open the sidebar. Select Styles (icon with an A), select the icon with the tooltip Character styles, click on the last icon in the row with tooltip New style from selection. Name your style, say bordered, check that inherits from Default character style and OK.
Now select some other characters, double-click on the character style bordered and it will get the border. This border should be saved in docx and remain on re-opening.
You should always save your documents in native open document format (.odt for Writer) and do a Save as on completion if you need to share a foreign format. Cheers, Al