My family member was sedated on propofol for 9 days in the icu and now she is slow to wake up. Is this concerning?

Possibly. Propofol is used for sedation in ICU because it wears off more quickly than other sedatives. Still, after 9 days in ICU there are many reasons why she might be slow to wake up. We would need to know more about what is wrong. Stroke, poor kidney or liver function, heart failure, metabolic imbalance are all problems that can impair mental function. The ICU team will do their best to fix them.