I clicked Next Turn button and game showed message box about critical error (while AI players were making their moves) and crashed several seconds later. I attach to this message log file and a file that, as I understand, represents current save (I may be wrong in a latter case, as there are numerous files in Save folder).
Thank you for your answer. I've made some research and found out one more person who reported about constant AI crashes after year 1919. I followed his advice and turned off option that allowed additional time to AI. Worked for me as well, at least for now.