Some Android phones do this and I haven’t yet figured out why! I’ll continue to look into it. Hopefully the web workaround will be ok for now.

Francois, I wonder if this is less a case of saving routes (downloading) not working but more a case of not being able to find the downloaded route?

My experience with supplied File Managers on my android phones has been less than satisfactory, especially for locating downloaded or transferred files. For years I have used a third party app called File Manager+ which is far clearer and more intuitive. 

I've just done a quick test on my Android phone: I created a route on the app, saved it, downloaded it. I can see it in my File Manager+ app but it is not visible in my 'downloaded' folder in the system File Manager. 

@Richard : yes it's a disturbing . For the time being i will keep using the workaround. Hope you will find out what is going on

@Hobbesontour: Nope. Gpx file cannot be found neither on my smartphone native file manager nor the one I actually use which is Solid Explorer