[ADMB Users] Diverging likelihood and maximum gradient component

[John]

I've recently run across this particular problem: the model is trying
to minimise a negative log-likelihood function (LLF), and makes steady
progress reducing the LFF. However, it gets to a point where it
improves the minimisation - i.e. the LLF value keeps decreasing - but
the maximum gradient component starts increasing again. Is there any
specific problem that can cause this effect?