It has been two months since I broke up with my ex-girlfriend. Yesterday was her birthday. I wished her a happy birthday in her circle of friends, but she didn't reply to me.

Breaking up is breaking up. It's normal for you to send a blessing, but it's not normal for people to reply to you and give you hope. Everything you say shows that your girlfriend doesn't want to get back together with you, so she won't give you such meaningless hope. I suggest you give up immediately, don't pester, learn to look forward, keep yourself busy, don't think all day, and slowly forget. Time is the best medicine.