AD7616 - software mode, serial interface - no register write update

I use the AD7616 in software mode with the serial interface enabled. Spi runs at 16.6Mhz.

Writing to a register and reading the corresponding value always results in a return of the reset value, not the value written to.

For the configuration register, always 0x0000 is returned.
For the input range registers (A1, A2, B1, B2), always 0x00FF is returned.

I've verified all DC voltages. Power consumption is also normal, both during reset and during active operation.
Enclosed a screen-shot of the spi-signals applied. In this example, I write 0x8833 to input range register A1 and expect to read 0x0033. The value I read is however always 0x00FF.
Yellow is CS, Green is Clk, blue is MO, red is MI. First screenshot shows the write action and 2 corresponding read actions. The next 3 screenshots show a zoom-in of those 3 signals.

Does someone know the cause of no write register update action?