The 'Support Me' button was created as a way for you to directly support the creators that you like and care about. It gives them a little bit of an extra monetary boost directly instigated by you! With that in mind, a user cannot use the 'Support Me' option countless times, as display has some has implemented some limitations on the button.
You can only use the 'Support Me' button 500 times per day. When you have reached your limit for the day, the button will become grayed out and you will not be able to click it. When this happens, you must wait until 12 AM UTC the next day to start using the button again.