I think she keeps treating him after the abuse to manipulate him, get the painting and get revenge and if she treats him and he successfully forgets about her she saves her own life.

To say that Frank just randomly comes up  with "hypnosis" as a solution to the problem is inaccurate. Frank goes to the doctor and ask for medication, remedies or nontraditional therapy  for amnesia. The doctor doesn't say hypnosis but it cuts to the scene of Frank telling Simon to choose a hypnotist which infers that…