If you contact a provider for the appointment and if we don't get any response. How many times should we try to contact again or let it go.

Then I figure she doesn't care to meet.

Make sure you've read her website/ad and contacted her according to her preferences. The only reason that I wouldn't respond to an appointment request is if it was offensive/explicit, or simply didn't include the information that I ask for.

If she's rude enough not to send you a quick note saying that you don't appear to be a good fit, you should by all means be rude enough to keep filling up her inbox with requests, especially if she's hypocritical enough to have anything on her website referring to the importance of mutual respect.

There are many reasons a lady may not contact you including a lack of professionalism. With that said, I've had some of my best experiences with a lady who is notorious for not getting back to gentlemen.  I simply contact her and if she responds, we have a good time. If not, I move on to another lady.  

I mean after all, she has to come out sometime, right?