@IndieGameCove’s comment is probably right on why you are getting this behaviour. Particles usually face the camera at all times, like billboards, if any axis is locked you will get a rotating billboard.
Another thing you could try is to check if the materials used by the particle system are double-sided or not. There is a checkbox you can tick in the material editor. If you can see the particles after ticking this box it will be because the particles billboards are rotating and not facing the camera at all times.