I suppose that you are running mysql as database server. There is option to log all queries and connected usere, but you need to restart mysql server with some new command line options. But I don’t think that that will solve your problem.
What would I do in your place?
First I would change all passwords including root password. If this happening every day at same time than it must be scheduled somehow. I would look at cronjobs. Then my own scripts, proccesses. I would also do a grep search on hole system with some keywords like table name that are dropped.