In reply to The Lemming:
Win 10, LR 5 for me. Saves tags to DNG files no problem and can be read within and outwith LR. Just tested again to check as I don't use DNG as a norm, but still works simply and easily. It does take time on my pc though so have to be patient to allow the saving.
My LR also tells me in the right side panel scroll down to metadata as to whether it has changed and so needs saving, or is up to date. Check that. Also try switching off auto and do it manually. I do not use auto (since I don't use DNG as a norm) and do a manual saving - prob why I get the warning metadata has changed and needs saving?
Sounds like you have some corruption or incompatibility issue. I do remember a while back finding and updating the win codec pack.
Anyway, I think others have given all the possible things that could be involved and help, so if it was me I would look to a corruption issue somewhere and possibly reinstall LR or more likely I would upgrade to LR6 (though I'm actually waiting for LR7 if it ever comes
!!).