Pivots don't refresh until you refresh them, so a pivot created yesterday on yesterdays data will still show the same today even though the underlying data has changed.
You could protect the sheet to prevent a refresh.
If you want to keep yesterdays pivot and have a new one for today, you could Ctrl+Click&Drag to copy the sheet tab and then refresh the copy.
Short of coping the data as values to another sheet or protecting the sheet seem to be your main options if I have your needs correctly understood.