Sometimes some messages appear in chat only for a few seconds, then disappear from the chat history completely.

There are two possible reasons
1. An engine message I'm not replicating
2. A message from another mod that's not using this mod's interface and instead directly printing to chat which unavoidably will get cleared away.

If it's just a message a player is sending, then I might have a bug in the friendly forces shared chat logic, which hasn't been well tested. Otherwise, I'm tempted to just blame the other mod for not being compatible with mine (which is likely since you have to go out of your way to be compatible)

Ahh I see, so it must be printing to the regular chat then. It's Milestones mod that I just noticed this with when it prints the initial new game message about which milesstones is loaded. Is there no way to view the chat log of these messages? I sometimes miss something that is printed from another mod and thus can be a bit confusing.

The whole way my mod works, is by keeping its own log of chat and basically faking it. I cannot capture what is printed to chat, so other mods have to go through my interface so I can.

In a unfinished newer version I have a GUI to properly view the (fake) chatlog, but I have been in a coding slump for quite a while now :/

If you want to try your hand at editing Milestones so your local version is compatible, I have a compatibility snippet in the readme that you should be able to just drop a call to into every object.print instance

Sure, but really I wouldn't want to hunt down every mod that has its own chat messages to fix it, not to mention redoing the fix if it ever updates.