What is refreshing my table in SQL Server?
Depending on the situation outside of what you have mentioned, you might be able to eliminate this problem by creating a new account on mysql and remove access to the db or the table of all other accounts.  Then you would have to update the system elements you want affecting that data.  This approach potentially is easy, but it also potentially is unfeasible.  

If you cannot do that, I'd recommend a divide and conquer approach.  There a lot of ways to divide this up.  My first impulse is to look at the following:

SEARCH FOR THE PROBLEM AREA 1:  INFORMATION SCHEMA
Search the information_schema for %tablename% to see if there are procedures, triggers, or foreign key constraints referencing that table.  Look to see what all those references are doing.  In the triggers and procedures I would look for DELETE on the table and if there are foreign key contraints affecting that table, I'd be looking to see what other tables having data deleted would delete records from the table where you entered data.

SEARCH FOR THE PROBLEM AREA 2:  APPLICATIONS TOUCHING THE DATABASE
I would search the source code for the tablename, again looking to see what each reference to the table is doing.  Depending how your application, if you have one, sets up its sql, you might be able to find the culprit by searching for "delete from tablename" to filter references that cannot delete anything.

SEARCH FOR THE PROBLEM AREA 3:  CRON
Cron could be running shell scripts referencing the database.  The cron statements could reference shell scripts that could be anywhere on a server with access to the database.

SEARCH FOR THE PROBLEM AREA 4:  PEOPLE
If other people have the permissions to have done this either directly or through their programs, how you handle this depends a lot on the nature of your responsibilities and theirs, and the relationships you have with them.  Asking around is usually a good idea, but you have to assume you might not get correct information that way. Taking away all permissions except new ones you assign is a good way to find out what is going on, but it is not always appropriate to take that sort of action, especially if you are junior to the person who permissions you eliminate.