There should be a little extension with a securing tab on the end. It's not meant to come out so they break when removed. The only way to get the arm out without breaking the tab would be to remove the dash and see if the tab can be freed after splitting the case. Found a pic, see below.
I have one that keeps popping out. It's one of the two in the pic (whichever one operates the defrost door). I just have to reach underneath and push on it as I alter the vent slider to get the vacuum solenoid to shift and align the lever with the hole. I could probably do with glueing it in place but I've never got round to it.
One of mine actually snapped off the lever at the star. I have it screwed together, and think i might have used a little epoxy to help hold it. I snapped it when I absent-mindedly changed the vent positions with the fan on full. I heard the air pressure building and realised what I'd done, but couldn't change vents or fan speed before the lever snapped. Since then I've made sure the fan is on the slowest speed when changing vent position.