Participants were presented with 32 images per category. However, some trials were lost due to artifacts. Though most of the time the valid trials hover around 30, the minimum number of trials in a particular category was 13 which seems very low. In addition, the number of trials in one category is significantly lower than the trials in the other two categories. What is the best practice for dealing with this issue? Should individuals with low trials be excluded from analysis? If so, how should the cut off be determined?
There's not really a clear single best practice. The only hard-and-fast recommendation I can give is that this decision must be made before you look at the results --- what you really can't do is try a bunch of methods and choose the one that gives the nicest-looking grand averages.
There are lots of options --- kicking participants out, keeping them, trying to clean artifacts (e.g. with ICA, etc.). It is not crazy to keep people with 13 in a condition (several published papers go lower than that) although it may be justifiable if they are qualitatively different/worse than others (e.g. if you notice they had really persistent slow drifts or something). But to be honest I think getting down to 13 doesn't sound particularly awful when you already presented such a low number of trials per condition. With only 32 per condition it's practically guaranteed that some participants are going to be pretty low.
You should read those two publications before you proceed ...
https://www.researchgate.net/publication/309293946_ERP_Reliability_Analysis_ERA_Toolbox_An_open-source_toolbox_for_analyzing_the_reliability_of_event-related_brain_potentials
https://www.researchgate.net/publication/308090589_Psychometric_considerations_in_the_measurement_of_event-related_brain_potentials_Guidelines_for_measurement_and_reporting
Article ERP Reliability Analysis (ERA) Toolbox: An open-source toolb...
Article Psychometric considerations in the measurement of event-rela...
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