Logitech K380 keyboard won't turn on!

Hello, I have a recent Logitech K380 pink keyboard (at least I've had it for 1 month) and when I turn it on with the button on the side, I see the green light for a few seconds and then it turns off while the button is still on, I don't understand!

I'm really upset, everyone talks about it positively and the batteries are supposed to last 2 years! I have tried to turn it back on several times but to no avail, and as a result, I can't connect it to my iPad because it says it's off, can you please help me? I really need it for my class which is in 1 hour!