How long should the battery last on the pen?

I'm running into an issue where I'll take my DPT-RP1 to a meeting with the device and pen fully charged. When the meeting is over I let the device fall asleep. The next day I'll go to use it again and immediately hey a notification that the pen battery is low. My meetings are.only 30-60 minutes.

Shouldn't the pen fall asleep too and the battery last much longer? I don't have draining happening on the device itself.