Indoor cyclist keeps popping out of clips
On Shimano SPD pedals, you can sometimes adjust the tension for how tightly they clip in (likely via a hex bolt). If the tension is too low, your feet will be too easy to pop out, whereas if its too high, you won't easily be able to get out (which isn't a problem on an indoor cycling setup). Try playing with this setting to see if you stay clipped in (turning the bolt clockwise should increase the tension). 

Also, there are two types of cleats  available -- single release (Shimano SH-51) which only release by turning your heel out and multi-release (Shimano SH-56) which release by turning in any direction. It shouldn't matter which one you use for indoor cycling (SH-56 is probably preferable for most people) but SH-51 might be an option if you're having trouble with SH-56. 

If you can't get the tension to adjust and swapping the cleats doesn't work (if you're using SH-56), normally indoor cycling bikes have toe clips available as well. You may want to use those. And work on your form.