In general, every request made from a visitor’s browser that hits a PHP script on the server uses some server power. Server power is a finite resource, so we limit how much you can use. And since we provide a free service, the limits are not very high.
The question “how much AJAX is too much AJAX” is impossible to answer for all sites. It really depends on how your website was built, how many people use it, and how often you query the server.
You’re free to use AJAX on your website. Just don’t try to host an application that rapidly polls the server for updates, like a chat script, with us, because you’ll quickly hit limits.
As to what you should do instead, it really depends on what you’re looking to do in the first place. Could you please explain a bit more about what you need so we can advice?