If that doesn't work, read the following, if you haven't already. I remember coming across this back in the day. In particular the example about variability across classrooms and using repeated instead of random option. Though I would first mess with the variance/covariance structure. Even though Jake said he would probably not mess with the convergence criteria, I would perhaps tweak it a little to let the model run a little longer.
Lastly per the classroom example, you may need to also accept there isn't much variation explained by the group variable that isn't picked up in a simple model. Also what is your group variable? is it a geographic location, if so, locations may be getting separated but they are tangential and actually more similar than believed.
Link:
http://www.theanalysisfactor.com/wacky-hessian-matrix/
Lastly per the classroom example, you may need to also accept there isn't much variation explained by the group variable that isn't picked up in a simple model. Also what is your group variable? is it a geographic location, if so, locations may be getting separated but they are tangential and actually more similar than believed.
Link:
http://www.theanalysisfactor.com/wacky-hessian-matrix/
My group is a geographical unit. The ICC was 3.7%, I don't know if that is a lot, little or whatever....
My random effects do not show the problem with the Hessian matrix. Only the estimate of the fixed effects.