To my knowledge, there is no nonparametric equivalent to mixed anova.
At best, I'm pretty sure in simpler models it is considered legitimate to convert all the data to ranks and run an ANOVA. I believe that the results for this are similar to running a rank-based test (such as a kruskall-wallis). I don't know if this still applies once you're trying to incorporate interactions.
A few other remarks, though. Are you sure you need to abandon parametrics? What is the non-normal distribution? How small are your samples?
And it sounds like your missing data problem may just be that Time Pressure and Decision Type are not crossed. You may be able to include both in the model, just not their interaction. If you're running it in a Mixed Modeling procedure (with data in the long format) rather than a Repeated Measures procedure (with data in the wide format), it should be less of a problem.
And if you're not following what I'm talking about, let me know and I'll clarify.