Digi has not made a newer Rabbit board that is designed specifically for low power consumption but it is possible to shut down various parts of the board with software functions in Dynamic C. There are functions to slow down the clocks, shut off any ethernet chip, shut down peripherals, etc.
See the programs in the Samples\LowPower directory. Some of the functions are:
set_cpu_power_mode() - sets the operating power of the CPU
pd_powerdown() - powers down the interface hardware, ethernet or WiFi
pd_powerup() - powers the interface back up
Mar 13, 2019