How can I draw persistent trails with particles?

I'm trying to make a particle effect, where I can use the particles as normal, but where they don't clear when travelling, effectively leaving a trail. (in a 2D game)

Right now I'm using a camera with a RenderTexture, rendering to a quad shown by the main camera. The first camera only clears depth. The effect is that the rendertexture records the particle trail. The problem with this is that it is pretty unreliable (the full trail of the particles often won't be recorded, only specific positions during the trail). It also feels like there must be a more efficient way of doing this.

Any pointers?

(The end goal is making a dynamic 2D paint splash - the particles all burst from one point, and by leaving a trail, they "paint". If you have any ideas as to how to do that with something else than particles, please let me know!)

Edit: What I've achieved with RenderTexture: The red one is pretty much how I want it (still needs tweaking on the paths and colors to hopefully look less like fireworks and more like paint), but if the framerate is low, it turns out frayed like the blue one instead. I'm targeting low-end machines and using WebGL, so the framerate will drop at times.