My daughter started propranolol for her lower lip H when she was 7 weeks old and was on it until she turned a year. She was taken off but has had considerable rebound growth. She was put on Timolol which did not do anything for her so last Friday she was put back on propranolol. Our doctor told me that she can use it for a total of 15 months. Because we had a 2 month break we can start it back up again but only for 3 months.
Your provider would give you the best idea of what they think is best for your little one. But, that's what ours advised us.