I would want to contact the developer of the mobile app.
We have no known issues with WebDAV. We use a few very large WebDAV clients to ensure all is operational. The most touchy of those clients is MacOS and its WebDAV implementation.
I just noticed that app might be a wrapper around and open source implementation. Might want to find another solution or possibly enable Exchange ActiveSync on the server which is more mobile / synchronization friendly.
Hope this helps,