Sounds like you haven't hooked up power to the four I2C busses.
The most common mistake on wiring up the I2C mux is forgetting to connect the power pins for each bus (nothing works without it!).
From the spec:
JP6 - I2C Auxiliary Power Pads
These pads allow you to hook up power supplies for each of the 4 I2C Muxed busses. Depending on your design, you may be powering the I2C devices on each bus from another power supply. In that case, you would leave these pads empty. Otherwise, you connect the appropriate power supply for each bus. For example, if you want all busses at 3.3V and the host is a Raspberry Pi, you would hook up VCC (from the Pi @ 3.3V) . You can mix 3.3V and 5.0V I2C busses by connecting the pads on JP6 to their respective power supplies.
JP7 - Auxiliary VCC connections
These connectors are all tied to VCC on JP1 / 3, the VCC from the host interface (usually the Raspberry Pi or Arduino)
Hi BP, just got my MUX to hook up all the cool stuff! However, when I connect to the Grove Connector board, it's not seen at all. Blue light indicating power to the board is present, but no-go, unfortunately. When running the test program, I get "IOError: [Errno 5] Input/output error" Not sure if I'm missing something obvious....well, I'm sure of that!