These are the limitations found in a two-way ANOVA: 

• It becomes difficult to maintain homogeneity of the blocks if the number of treatments is large enough. 
• The technique can be challenging and time-consuming. 
• In order to get accurate results, a missing value cannot be ignored. Certain adjustments must be made in the analysis after replacing the missing value with some function of the existing values. 
• Analysis becomes increasingly more complex and interpretation more difficult when the number of the factors are increased in a study.