Board Game Arena

In turn-based games, the game record is very important, because you need to see the actions of the opponent's turn, but the opponent's actions cannot be seen in the current record, I hope it can be improved

It is by design, as the game editor asked for this feature.
You should be able to see everything that happened since your last turn, but not further. If you want to check what everyone else did, you must do it before your own move.
The game editor wanted this game to emphasize the memory part of the game.
In turn base games, nothing prevent you from copying the relevant log info into your personal table notepad.

it happened to me several time when this game is played on a turn based basis in tournaments that I could not even see the las t move from my opponent.
I was playing on my mobile device, not sure if this is would be different than playing on a computer webpage.

Ran into this same issue. Game is unplayable async since you can have an opponent take a turn that never hits your logs at all.

Logs disappearing after you take your next turn would be one thing, but that is not what is happening. Playing turn-based-async this means you can end up taking a turn, closing the window, and coming back for the next turn where you can only see 2 of your 3 opponent's actions. There should at least be a warning about this in the How to Play or an option to turn logging back on. The memory concept is fine but you can't memorize an action that you never see.