change in variable importance
Probably you can use multiple decision trees - each for slice of dataset. Then combine the results from each decision tree. You can also weigh the results from each decision tree. Eg the dataset for 2015 can be given more weight than dataset for 2014. I do not see much harm in spliting dataset and training different trees as it helps to account for the predictor values in a more accurate manner. If you could more details about the data or the "variable" you mentioned, people would be able to help more.