I agree with everything that has been said above and I think it really depends on what you would like to happen to the friendship post wedding. Do you plan on eventually rekindling this friendship or would you be 100% okay with severing ties?
I was in the same situation. She was actually asked to be a bridesmaid and had initially said yes, but then no with a million excuses that were aimed at making me feel guilty about having a DW. Our friendship had been pretty rocky for years but I looked at the whole thing as my last attempt. In the end, I did not send her an invitation. I just refuse to focus any of my energy on negativity during this process. I do have other friends who I knew would not be able to attend, but I sent the invitation regardless.
I agree, there is only so many attempts that can be made.
The girl who I thought was my bestfriend wouldn't even talk to me about my engagement/wedding. The friendship dwindled to nothing shortly after I got engaged. I gave them an invite but never got a response. Since it was so strained I didn't even get to ask her to be my MOH. I tried a couple times (dress shopping, advice, etc.) and I got every lame excuse in the book. I made one last attempt with having her help plan my bachelorette and got such a ridiculous reply that I gave up and haven't talked to her since June. She also 'forgot' my birthday and I was just over it. My life feels so much less stress without her in it. I hate to say that, but it's true.
Then I had other drama surrounding invites from another friend -- oddly these two I am talking about are friends (we are all neighbors) so you have to wonder if that is fueled so how between the two of them. High school drama I say!