Sorry, but this is nonsense. This is the bug report forum. It's absolutely the place for this.
That being said it's the same for everyone I talked to. Defenses are not logged. This is how it looks for me. As long as I stay online I see my defenses, but as soon as I open the game again it's the same defenses as can be seen on the picture.
This is starting to really annoy me. I've MUCH increased my arena defense like 3 weeks ago, and I would LOVE to see the results of that, but can't because I sit at 3'199 and have no idea how many defenses I win. Sorry, but please fix your damn game. There's bugs all over the place. Multibattle autosell not working, disappearing champions in autobattles, game freezes, arena defense logs, what have you.
Thank you.