I have had to make loops like this in the past, mostly for animated textures etc. What I do is render out a section that is 2 times as long as i need, that has the full animation in it. So for you if you want a 100 frame loop, and it takes 100 frames for your particle system to complete it's spline path, then you would want to render out frames 100-300.
Now using a compositing program, I use After Effects, you will want to cut your animation into two sections of 100 frames each. Then layer them in your compositor / editor. Now take the one that is on the bottom, and split that in two sections of 50 frames each, and then flip their positions. If you loop those two clips, you will have a seamless edit at the loop point, and then have a break in the middle of your clip. This is where that second section comes in. Blend into the the second clip when the first one's loop point is. Because the two clips are offset, you will have a clean section to cover up your edit.
Hope this works out for you