From what I have read so far, the condition only seems to get better when the child becomes a teenager and is able to control it a little more themselves. In response to Laura Hallam's response, I too am interested if the general feeling about the operation being worse than the original condition runs true with most. My daughter was born in June 2000 and she has Marcus Gunn jaw winking with ptosis. I was able to recognize the conditon at birth and this was later confirmed by an ophthalmologist. My daughter is now 10 months old and she is healthy.
Ophthalmologists here think that nothing can be done.
We are naturally concerned about her future at school and in life. Hearing information about other people's experience in this forum makes us feel somewhat comforted. However we do hope that somebody out there has some good news that something can be done about this condition. I don't know where you live, but my Opthamalogist is definitely telling me that he can perform a surgery to correct my daughters lid, with NO adverse side effects. He is however, advising us to wait until the jaw wink diminishes somewhat.