In your specific case and pic you can set the skirt to print further out away from the part. I do this when I have supports. I do the print preview and look where it is and then set the distance further out from the part and look again and adjust until it is where I like it.
Sometimes if I have small diameter supports kind of like in your pic I may try to have the skirt under then and also make the skirt wider to add sort of a base for the small supports in hopes it helps to hold them!