This works:
UPDATE myTable
SET myTextColumn =
REPLACE(
REPLACE(
REPLACE(myTextColumn
,' ',' '+CHAR(1)) -- CHAR(1) is unlikely to appear
,CHAR(1)+' ','')
,CHAR(1),'')
WHERE myTextColumn LIKE '% %'
Entirely set-based; no loops.
So we replace any two spaces with an unusual character and a space. If we call the unusual character X, 5 spaces become: ‘ X X ‘ and 6 spaces become ‘ X X X’. Then we replace ‘X ‘ with the empty string. So 5 spaces become ‘ ‘ and 6 spaces become ‘ X’. Then, in case there was an even number of spaces, we remove any remaining ‘X’s, leaving a single space.