There would need to be informed in a database in order for the button to know if it needs to be pressed.
I would suggest either using an Ajax request to do an insert statement into a database once the selected button is pressed or you can use it through a tag submits into an insert statement in order to get the data to see if it should be permanently selected.
Then you would need a select statement to read the database data into an IF statement such as this;
($row['Button_Pressed'] == '1' ? 'Selected' : '')
The Button_Pressed is just the column in the table that would store the data and the 1 is the boolean value