Whenever you bring up the property screen for Counter items, the "Infinite item" selection changes.
For example, say I set it to (None). Next time I look at it, it'll display Rupee (1). Then, if I don't touch it, and dismiss the window with OK, it'll display Sword (Level 1). Repeat ad infinitum.
Edit: Unrelated to the bug, I assume that the "infinite" item is one which, when picked up, will cause the counter to display Infinite.