If DevTools is not open then the sent requests are not saved, if DevTools is open then only the requests are saved/logged in the Network panel. (Although this is not same for JavaScript/Console messages!) If any error occurs on server or to know the response of the server for the last request then developer has to re-request to see what is/was the error/response.
Either all requests should be logged/saved in Network panel, or at least last POST and AHR (XHR) request should be logged/saved after the last loading of the page even if the DevTools is not open.
An option in DevTools' settings may be provided to select the kind and/or input the number of request to log/save.
I have requested same feature for Chromium too:
https://bugs.chromium.org/p/chromium/issues/detail?id=1136198