When a proxy is bound to a specific IP Address the proxy will switch itself off if the device looses that IP Address assignment. This is in the interest of conserving battery power. You will need to restart the proxy server once that IP Address has been regained.
When a proxy is bound to the all interfaces IP Address (namely 0.0.0.0) the proxy will continuously remain on as the internal 127.0.0.1 IP Address is always available. Binding a proxy to 0.0.0.0 will only expose the proxy to other devices on the externally available IP Addresses (namely all IP Addresses besides 127.0.0.1) and not on 0.0.0.0. The externally available IP Addresses are displayed once the proxy is started.