There is no deep sleep mode in rev D. Using the same operation sequence on the low power, both rev of AP2 can work on sleep mode.
Once an ANT channel has been opened, ANT can only operate in one of two states: ACTIVE and SLEEP.
ANT will transition to the SLEEP state any time it is waiting for an SRDY pulse from the host MCU.
In rev D, the AP2 can be entered to deep sleep mode by sending DEEP SLEEP command if the synchronous message protocol is implement properly.
There is an AP2 errata on our website
http://www.thisisant.com/images/Resources/PDF/ap2_rf_transceiver_module_errata.pdf
which shows the known issues on these two revs.