Why won't my back stay clean and clear of acne even though I keep good hygiene?

Not related. Acne is a chronic, serious, non-lifestyle-related disease and it's both cruel and stupid to tell someone with the disease that it's from poor hygiene. You need a physician's care. Acne on the trunk won't respond sufficiently to topical rx though benzoyl peroxide is a good start. You'll need systemic rx, either an antibiotic or (the big guns) isotretinoin.