Hmm, I'm not entirely sure I understand the problem. Could you attach pictures to the post so that it will become clearer?
And maybe also give the icing recipie you use, how exactly you prepare it, what consistencies you define as thin or thick, how thick the tip you are using is exactly. All of this could be the reason.
I normally don't have trouble with clogging, no matter if I use flood consistency or piping consistency icing. So my first guess would be that you don't sieve the icing sugar OR that you allow the surface of the RI do crust and then fill it into your bags. Both of this might cause lumps in the icing and therefore clogging. I've read that filtering your icing through an unused nylon stocking helps to get rid of that. Then you could thick the icing up to the required consistency for piping clean borders without clogging the tip.
But I could also be totally wrong and something else causes this, as you don't provide enough information to be sure 