I tried to save a WG84 shapefile as a UTM 16N projection and got the following error: "Export to vector file failed. Error: creation of layer failed (OGR error:Failed to open Shapefile `HF patients who are not 30 day readmissions in UTM 16N.shp'.
As @Andrej wrote in his comment, a shorter name without whitespaces should work.
Otherwise, I would also check the path length to the directory where the shapefile is to be stored. I have already have issues with long paths and solved them by saving my shapefile on D: directory (for instance).