No response from recommenders after they agreed to write recommendation letter I am planning to apply for green card for which I need recommendation letters from well known researchers/professors. In February 2019, I had contacted one professor and one industry based researcher to write the letters for me. Both these people know me through my research and have frequently cited my paper. At first I did not get any reply from them. A week later I reminded them while copying my PhD advisor in the mail. My advisor knows both of them. I got immediate reply from them that they would be happy to write the letter if I could given them an initial draft. I think it is OK to copy your PhD advisor while asking for recommendation letter from independent people who don't know you personally but only through research and papers. 

Anyways, A month later i.e. in last week of March, I gave them the draft. Since then, I have sent 3 reminders to them but have not heard back from them. I am getting anxious and don't know what to do.
Does no response after 3 reminders and 2 months mean they backed out? Is it ethical?

I have all the documents ready for filing my application and I am just waiting for them to give me the letter. Since there is no deadline to apply for green card application, I can't even provide them a deadline. But I have tried to convey my feelings about the delay using mild language.
You need to move on and find new references, people who actually know you.

Realistically, it's hard to imagine anyone wanting to write an LOR for someone they've never met and know only as a name on a paper they've cited.  But then you further poisoned the relationships by waiting a month to respond to their requests for a draft (of the letter you want?) and CC'ing your advisor on your requests, as if to "report" them for not responding quickly enough.  And who knows what you put in your draft or your "reminders".

If someone did that to me, I'd permanently ignore them.  I certainly wouldn't waste my time recommending them.