Hi CW,
You can use the PGroup or the Standard Emitter to feed the Object option in a Cloner Object (MoGraph).
Then use a MoGraph Cache tag and bake on a sequence. Then loop this with the cache options. You might consider to set up several of them to overlap—time wise.
A loop option in Thinking Particles is not natively given.
I would create three or four very short, but complete sequences. (Complete: From emitting to hitting the ground) Then render these and compose them in After Effects on top of each other in a nice random mix.
60 seconds for a confetti rain sounds not a lot of rendering (confetti as I understand it, may have no reflection nor refraction, so it is fast)
All the best
Sassi