Check to make sure that you do not have a singularity anywhere in the model. For instance, a constraint or load at a point is a typical one. This would make the stress graidients very large, there by forcing mechanica to move to most likely the max p order of 9. Also, see if you can simplify large regions of relatively think material with shell elements insead solid elements. Also, if you are interested in the stress in a particular region of the model you can always create measures in that region that track the value of the measured quantity. That way you can check to see if those critical regions are converging on stress or displacmenet. Mechanica also makes is such that instead of trying to converge the model globally (which is the default) you can for the p-element convergence to take place with respect to a given set of user created measures. I have analyzed some pretty huge models in the past (e.g. 30,000+ elements). But that was only possible due to the analysis converging with a max p order of 6 or 7.