In some cases, Prism will say the following in a yellow floating note: 

"Some results are missing because estimated variance-covariance matrix is not positive definite." 

Prism will still show some results, but probably not the ones that are most important to you!

The message won't mean much to most scientists. Neither will this alternative wording:  

   "The Hessian matrix is non-invertible. It is not possible to take the square root of the matrix. "

Basically, this message  means that Prism was not able to complete the analysis given your data and choices. Given your data, the model is too complicated.

Possible fixes or workarounds:

•It might help to go back to the RM Analysis tab of the parameter dialog and tell Prism to remove terms from the model when the variance would be zero or negative.

•If there are no missing values, use repeated measures ANOVA rather than fitting the mixed model. 

•If both factors are repeated measures, try a model where only one factor is specified as repeated measures. If only one factor is repeated measures, consider ordinary ANOVA. The whole point of a repeated measures design is to have internal controls so variation among participants/animals/plates... is factored out of the analysis. But if there isn't much variation, the repeated measures analysis may not be needed. Graph your data and see how much the participants/animals/plates... differ from one another. 

A note if you use Satterthwaite or Kenward-Roger degrees of freedom

The first fix above has a cost worth knowing about. Satterthwaite and Kenward-Roger degrees of freedom cannot be computed for a model with a term removed, so if a random effect turns out to have an estimated SD of zero, Prism falls back to the Legacy method for that result and posts a floating note. Selecting Restrict the variance to zero and keep the term(s) instead keeps the term in the model with its variance held at zero, which both preserves your chosen degrees of freedom method and often avoids this message in the first place.

Even when the analysis does complete, a variance component estimated at or very near zero makes the small-sample corrections unstable, whichever method you choose. See denominator degrees of freedom in the mixed model.