There isn't a way to save it with the quotations. There is, however, an ugly method to put quotes back in.
Insert a column to the left of column A and between each column of your data. Fill-down the empty A column with "FIRSTQUOTE" (not in quotes) to the bottom of your data. Fill the columns between your data with "INNERQUOTE" (again without the quotes) and in the column to the right of your data fill with "ENDQUOTE".
Save your file as a CSV.
Open the file in Word (or any text editor) and do a find-replace "FIRSTQUOTE," (note the comma) with "
Find-replace ",INNERQUOTE," (note the leading and trailing comma) with "," (quote comma quote)
Finally replace ",ENDQUOTE" (note the leading quote) with "
Re-save the file. As long as the words FIRSTQUOTE, INNERQUOTE and ENDQUOTE didn't appear in your data to star with, you should have a quoted CSV file.
As I said, an ugly method but it works.