This started happening to me in a big way around January of this year, mostly while dualboxing but also while playing solo. Sandbox does absolutely nothing, clearing chat logs out of the temp directory does nothing, its not battlemod as its not running. I remember it happening very rarely before that, but now its aggrevatingly common. Doesnt even need a full chatlog, I can have the log break just after login and stay broken until all instances of FFXI are restarted, only to break again immediately.
Whatever changed, it changed relatively recently, and this issue is absolutely pushing me to communicate via Discord more than in game chat.
sounds like a different issue, i think OP doesn't have to restart, it just randomly flushs all previously received chat massages out but you are still able to receive new ones without restarting ffxi.
its a very old bug and i'm not even 100% sure if its related to windower or if it doesn't also happen with vanilla client.