Is SRAM erased when putting Arduino into sleep_mode_pwr_down?
Generally, Atmega sleep modes do not erase RAM. Their memory is static and as long as voltage (above 2.7V I believe) is applied, data is held.

However, this also depends on how you plan to wake up the device.
If it receives a RESET, RAM is cleared and program execution starts from the beginning.


  If an enabled interrupt occurs while the MCU is in a sleep mode, the MCU wakes up. The MCU is then halted for four cycles in addition to the start-up time, executes the interrupt routine, and resumes execution from the instruction following SLEEP. The contents of the Register File and SRAM are unaltered when the device wakes up from sleep.


Check out the AVR's sleep modes to see which fits your application best and how to safely wake it up again