。
She makes sure no one ever forgets her clean-cut image.
Literal
She [topic-は] refreshingly-clean did own [genitive-の] image [object-を] forever cause-not-to-forget [explanatory-のです].
The verb 忘れさせない is the negative causative of 忘れる: 忘れる → 忘れさせる ('cause to forget') → 忘れさせない ('not let forget'). She is actively preventing others from forgetting. すっきりした is the past tense of すっきりする ('be / become refreshing, clean, neat'), used here attributively to describe her image — '(her) clean / well-defined / no-frills image'. いつまでも ('forever / ever') stretches the prevention indefinitely. The closing ~のです (the explanatory particle) adds the sense of 'this is the situation / explanation'.