The staff cant give you free gym badges, especially if you dont have a screenshot. did you do the battle at exactly the same time? perhaps the server is autorebooted at some point (i think it does this at 12PM UK time) try waiting an hour after the 24h is up and then battke, or better ask the staff if they plan on restarting the server soon. progress is saved at 5-10 minute intervals and when you log off, so once you have completed the gym battle and have gone back to the map, log out using the red 'X' in the top right corner of the window, then log in again and your progress will be saved (*MAKE SURE THAT YOU CAN SEE THE NEW GYM BADGE IN BAGPACK>BADGES BEFORE YOU DO THIS!*)