How are you running the so called proxy. Is it something in the browser. For browser based traffic you really don't care if the proxy changes. In many cases it does when you do something as simple as close the web browser. This is not something you can really control since is a extension of the browser.
I am unclear what exactly you are calling a proxy. A true proxy server will actually compromise the security because HTTPS is end to end encryption and having a web server in the middle means you can not do end to end encryption.
Many of so called proxy are cut down vpn services that only do web traffic. There is no such thing as a "free" service. They all must recover the costs of their internet bandwidth and server...