Here is what finally worked: 1. Read the EPROM many times (11 to 19) until the checksum is constant. 2. Now the content can be read perfectly for all EPROMS. 3. When I turn off the GQ-4X, then when I turn it on, I have to go through the above step 1 until the checksum is constant.
I tried it on two PCs (one with Windows XP, one with Windows 10 with a fresh install of the software): the behavior is the same. I wonder if there are capacitors or other components that are aging? I bought the GQ-4X new last summer (2015).