Hi Marco,
Thanks for the file
Sorry, that is not something that can be solved. Except the particles fade in and out during their travel or fake it.
If you have varying speeds inside of that, the time it takes to find a loop point will take very long.
That follows the “least common multiple” or LCM, with hundreds of particles and each perhaps in a different speed that will not fly with 240 frames or anything not significantly larger than that.
If you would have particles going through it with these four numbers (time to go through in frames) alone: 11 13 17 24, the LCM would be 58,344. Now take hundreds of them, and you get closer to infinity than to 240 frames.
You need to get groups to have a speed that is a pure fraction of 240 frames. The Rate is crucial here (no variations!). 100% means that it cycles per second one time. If you have 240 frames and a 24fps project, values of 10%, 20%, 40, and 50%, for example, will work. Note that frames zero and 240 will be the same! So, the project needs to be 0-239.
These can give the illusion of 240 frames looping while kind of having a varying speed. I left 240 in the example, so you can compare it.
Example
https://www.amazon.com/clouddrive/share/2VdoEDbmS5EnUvbxlRP4lmeT2WRCQMMiwlhfjjkIDeV
All the best