I've heard of the spoon thing before, and it will probably pop up with a quick Google search if you are looking for more detail.
Here, polyamory isn't really being described as a disease. Essentially, the spoons represent what GalaGirl might call one's buckets. If they are empty (or you run out of spoons) then you don't have the energy or ability to deal with life's difficulties as well.
I think that what Cattiva is trying to say is that ones spoons (buckets) need to be properly tended in anyone's life and more particularly so when one faces a challenge or difficulty that could tend to strain them, such as a disease OR juggling multiple relationships.