The Notecard does not need to be put into “deep sleep”, per se. Depending on the model, when it is inactive, it will automatically drop down to only consuming around 8-20uA.
For this reason, the Notecard is designed to remained powered at all times. If you cut the power, then you risk losing queued Notes, and this is an unsupported path.
You may find interesting that the Notecard has an ATTN (attention) pin that is designed to respond to several events, including a timer. The host can request the Notecard set the ATTN pin for x seconds. When you tie the ATTN pin to the EN of the host (or use it to drive a MOSFET), then it works as a sleep function for your sensing electronics while the Notecard idles at 8-20uA (less than the discharge rate of a typical LiPo battery).
Best,
Zak
Here is a similar Q&A you might find helpful: