After a brain infarct, my dad is unable to open his eyelids on his own. Why?

Hello,

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As you have described, your father had brain infarct after that he developed all symptoms related to eye right. So let me explain you that in case of stroke or infarct in the brain there will be involvement of cranial nerves also. The cranial nerve which is responsible for elevation of eyelid will also get affected in such situations like stroke. So the same thing has happened here in your father's case. So for treatment of his eyelids, only surgery you can plan but you should consult oculoplastic surgeon for that. He is the one who will measure all the parameters and depending on that he will tell you which surgery he should undergo. So my advice is you should take your father to an oculoplastic surgeon for this problem. I hope this helps.