How can I fix this fountain and prevent it from happening again?
Tie it down.

Here is your fountain.  You can tie it down across the white base which I assume is attached to the plastic fountain bowl and statue.  You could use a nylon or poly rope of some color you thought was unobstrusive.
You could tie the rope to stakes and then hammer the stakes all the way into the ground then put the mulch back on top.  That would make sure rope is tight.  I show 2 ropes but you could use 4.