The reason for this drop can be found in an alliance between two nations. In the moment they agree to an alliance, the arithmetic average of both nation reputations is calculated. You lose reputation with one nation and gain it with the other.
Nation A 80%
Nation B 40%
Nation A -20% = 60%
Nation B +20% = 60%
Unfortunately an alliance always will catch you off guard and it can be very annoying if you lose the option to talk to the viceroy because of it… I do not have any hint how to see an upcoming alliance.