The number one reason most Instax cameras stop working is that the batteries need replacing. According to the manual, you can take an average of 100 shots with two new AA batteries (or around 10 rolls of film) so it is worth keeping track of just how many you’ve used up so that you can avoid any nasty surprises.
Fujifilm also advises buying batteries of the same brand/type and only using alkaline batteries.
If the batteries are dead or dying, one of two things can happen: all the lights on the adjustment dial will blink simultaneously or the red lamp will light up beside the viewfinder.
When all the lights blink, you must replace the batteries with brand new ones while the lens is extended (on other words, with the camera turned on). Note that if you replace the batteries while the lens is retracted, the lights will continue to blink.
If only the red lamp comes on, simply turn the camera off by pushing the lens back into the body and replace the batteries. Provided that the camera isn’t damaged, this should do the trick.