I was doing a BASEMENT run and I got the D6, D20, and D4. Before breakfast, I used the D4 a few times and after a few more rolls (D6+D20 rolls), I got breakfast. I went to the next level and to my surprise, there were still items that weren't breakfast. I even picked up the small rock, which I distinctly remember picking up earlier in the run. Could the small rock have been put back into the item pool by the D4?
Hence, you can never get this item by D4 (or D100) rerolling.