Do you announce when you have lost due to Insanity?
Your insanity condition is secret, and you are forced to keep it secret.  The rules state it cannot be revealed to the other players for any reason, unless some other event tells you to.

So even if you have been put into situation where it is impossible for you to fulfill your personal Insane win condition, your investigator hasn't been eliminated and the game hasn't ended.  Your insanity, and your win-lose status, remains secret, and the other players will continue to eyeball you and wonder what you're really going to be up to.  This may or may not affect how quickly they can complete the investigation, so it is still important.