Indium may well resist nitric acids, other rare impurities may as well. Or you're seeing something refractory to this procedure, like glass or silica, or plastic.
Try to do this systematically. First try aqua regia -- adding a little HCl to the solutions containing excess nitric. See if it helps, and be alert, it may make cause a worse precipitate. Don't do it backwards, HCl before nitric may work too, but may also form a resistant precipitate.
Do evaluate all your solutions via ICP. Maybe you can prove conclusively that the precipitate isn't significantly affecting your accuracy.