If we are talking about system passwords (router or otherwise), there's a good chance you'll just be left with something malicious (ex. key logger) that is going to render null your irregular change of passwords. Regardless, irregular updates is just another form of security by obscurity. What if your password is cracked at the beginning of an irregular cycle?

The only reason one should have to change their password is if it is significantly weak -- "crackable" -- or they enter it manually -- it is visible -- in front of others a significant number of times for them to "record" the strokes. Good password managers, more or less, solve both cases.