The answer is almost certainly a solid: No.
The length of time that a client is willing to wait until it receives a response from the server is fully configurable by the client. Either the HTTP library being used by this app has a short time set by default, or the app itself has configured the request to have a short timeout. For an example, see this documentation for how you would set the maximum wait time for a request with CURL. If an app has set a maximum timeout of, say, 2 seconds, then there is nothing you can do at the proxy level to make it wait longer.
If you were running the app in an emulator you would have more control (because you could effectively pause it while you did your thing), and if you rooted your phone you may have a way to trick it, but there isn't anything you can do purely at the proxy level.
Your only option will be to figure out how to modify the response quickly, either by pre-setting the response in your proxy, or by some sort of scripting option.
Also, as a general rule of thumb a minute is a long time in the modern network world. In my experience even 2 seconds is a slow response. I would expect most clients to have a default timeout measured in seconds, not minutes. A mobile app that is built for high performance may use an even smaller timeout if the developers know that their API endpoints will return very quickly, and don't want the user to have to deal with a laggy experience.