Are people with acutely recovered cerebral ischemia more unstable?

Depends. Well unstable compared to whom. If you have recovered, we ordinarily would say you are stable but anytime a person has had ischemia, they are more likely to get a recurrence than a well person. And what is the ischemia secondary to would be an important question. Has the cause underlying the ischemia been corrected?
Likely. Acute stroke stabilizes over some weeks as measured by brain scan, MRI etc. Until then reoccurrence, instability may manifest with blood pressure or medication changes. Finding the root cause and treating that if possible is also, stabilizing!, .
Art of prevention. Once stroke has occurred, difficult to repair damage, and there are complications to deal with. My approach is first use Aggrenox and Lipitor (atorvastatin) generically to protect, search for unique causation if pt lacks history of hypertension, diabetes, high triglycerides, carotid stenosis. (such as anti-phospholipid antibody syndrome, hyperhomocysteinuria, mthfr mutations).