Hi Tao,
Finally we figured out the problem: removal of duplicated repeats.
Recalling the image I sent previously, the largely enriched region to the right contains lots of duplicated reads while the region to the right contains just few duplications. When MACS2 is run, because of the removal of such duplications mostly affecting the region to the right, there is no longer an enrichment and no peaks are called.
If MACS2 is run without removing duplicates, then we get the expected behavior: peaks are called in both the left and right regions.