I lived among people like that intermittently for much of my life. Many of them see your “thank you” as an opening to invite you again. To get rid of them you need to stop thanking them for inviting you. You may have to get very direct bordering on impolite. “I am not going to attend church with you. This is not open to further discussion.” Then bean dip. If your pest continues to talk about her church again walk away.
Yes, that may end the friendship. But if every conversation includes an attempt to convert you the friendship is already in bad shape.
(Yes, I know I'm not as polite as most of you. That's why I mostly stay logged out and read. Maybe I can learn something.)
I have to agree. OP, you have been very polite. It hasn't worked thus far. Now, you have to get firm.
I used to live in what I called the Bible Belt of the North (a city with many zealous fundamentalists and evangelicals). I finally just had to move because I couldn't stand it anymore. I am the same race and I am straight, so they assumed that also meant that I held a lot of their beliefs. I did and do not. Once we planned to have a family, I told my DH that I would not raise children in that city because I wanted my kids to be exposed to more than just one way of thinking.
I advise that you do not JADE (justify, argue, defend or explain) your position. Just firmly say "You have invited me before. My answer is and always will be no. I am not interested. Please, do not bring this up again." If you get anything other than a verbal confirmation that they heard you, if they start saying "But..." smile, and firmly say "Please, excuse me" and just walk away.
I wouldn't want to JADE because I don't want your daughter to be branded a heretic or anything at school. There could be repercussions for her. Let them wonder what religion you are or are not. After that, if they ask you again, just keep repeating "I said I was not interested" and excuse yourself.
Next, be prepared for them to try to have your daughter for sleepovers on Saturday nights so they can take her to church with them on Sundays.