I see similar to roger64. I had a look at writer2xthml and it is quite out of date and only in beta anyway so I took your text and re-created it using LibreOffice 4 with the Writer2Epub extension but with a few spaces changed to what LO uses for non-breaking spaces (control-shift-space).
When I looked at the epub file generated all the non-breaking spaces from the odt document had disappeared and there was only one present - a placeholder in a blank line :
not something I intended but clearly something that the conversion had inserted. At least it proved that if there had been proper html entities where I had put them they would have been visible.
HOWEVER where I had a non-breaking space in the original it had A000 rather than 2000 as the hex value in the output.
So I then re-examined your test document and found the same - all the non-breaking spaces are coded as A000 rather than as an HTML entity.
It appears the "deprecated" Sigil would convert the A000 to whereas 7.2 doesn't.
BobC