Checking the source code of the Azure Maps leaflet control there does appear to be code to handle token expiry when the map is reloaded and the token is retrieved from cache: https://github.com/Azure-Samples/azure-maps-leaflet/blob/7d9786a050549e440ddb78252949689f03215574/src/internal/AuthenticationManager.ts#L259
That said, I think there may be some room for improvement. It looks like it doesn't monitor the expiry time of a token retrieved from cache. I've just pushed an update to that project that should handle this better. Grab the latest code from the dist folder of that project.