This occurs because you forced font size “manually” (aka. direct formatting) using the size menu in the toolbar.
Whenever you enter a new cell (an empty one in same row or automatically added empty cells in new row), paragraph style for the new cell reverts to Table Contents with attributes values as defined in the style.
If you want to make your change persistent, modify Table Contents paragraph style.
If you are not familiar with styles, read the Writer Guide available for download on the documentation page of LibreOffice.org. This is an excellent reading to master the tremendous possibilities offered by Writer.
EDIT after reading carefully bug 115573 report:
Tables work as I expect here but bug 115573 mentions it is related to table styles.
In my opinion, table “styles” are presently templates rather than styles like paragraph, character, page or list styles. You can’t tune your tables once they’ve been created just like you can do with styles. Note, for example, you can’t create your own table “styles” nor modify provided ones, meaning only built-in “styles” are accepted by LO Writer.
This is why I prefer to create my tables manually (equivalent to Default Style) and massage them until I’m satisfied. Then if two tables must be similar, I copy/paste the first one to the appropriate location.
I personally find the present table style too “flashy” to be used in technical papers or other “official” (boring?) documents. In another question about table styles (I can’t find the reference immediately), one of the LO gurus admitted the feature to be rather experimental. My advice would be then to keep away from it and wait until it stabilises and matures toward integration into the other styles design.
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