The Listify theme has been designed to be as fast as possible and we are continuously working on making it even faster. It has been developed to handle unlimited number of listings. However, when running a website, there are many different factors that affect the performance, and the main one will be your hosting provider.
If you are using a low end hosting provider (usually less than $10/month) things may be slow. This is because most low end hosting providers are on a shared hosting environment, which means you have limited number of resources to perform the searches that Listify requires.
If you invest in a decent web host that offers server side caching and is built specifically for WordPress then you should not have any issues with speed.
Keep in mind that if you have a large number of visitors, you may need to invest in an even better hosting as the resources required to handle all the visitors will increase.