As a test, I sent ten /msgs from my multi to my main, "test1" through to "test10", with only the time to type them out between them. My multi was running in regular KoL, on Chrome, and my main was using just the relay browser, in Firefox.
Seven out of ten messages got through; test1, test7 and test9 failed.
I thought it might have been something like network congestion causing messages to die, but that seems unlikely now.