I try to move the messaging from the dating site to my phone by the third email. Women usually get many messages a day on a dating site so it is fairly easy to get drowned out by all of the other horny guys.
If I were you by the second or third email give your phone number and ask for the girl’s so you can continue to text them or call them if you want. If they do not give you their phone number then most likely they will move on or are not really interested in meeting guys online.