The generic 16x2 LCDs using an HD44780U compatible controller does not have to be, and should not be, refreshed. Once you write a character to the display it remains there, with no further action from you, until you either overwrite it with new information or you remove the power.
In order for us to fully understand what is actually happening you should supply us with a listing of the code that you are using along with a photograph of your setup.
Don