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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. 

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