My boyfriend is clinging on to an ex for dear life. Should I be concerned?

My boyfriend got out of a 2.5 year relationship about a year ago with a woman who dumped him because he didn't want to marry her (he wanted to eventually someone with a same cultural background). They have mutual friends and he is desperate to be friends with her, although she is very clear about the fact that she has no desire to be friends at all. According to text messages (before she blocked him), he keeps complaining about the fact that she is avoiding him and is cold towards him.

Should I be concerned?
My boyfriend is clinging on to an ex for dear life. Should I be concerned?
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