I confirmed the problem.
It seems like power saving code of Bluetooth firmware doesn't work with HHKB JP for some reason. I'll fix it later, use the following work around for a while until that.
WORK AROUND for 'BT controller for JP'
comment out 'POWER_SAVING' macro and compile firmware.
make -f Makefile.rn42 KEYMAP=jp
diff --git a/keyboard/hhkb/config_rn42.h b/keyboard/hhkb/config_rn42.h
index 21e73f1..ef63ad5 100644
--- a/keyboard/hhkb/config_rn42.h
+++ b/keyboard/hhkb/config_rn42.h
@@ -51,7 +51,7 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
#define BOOTMAGIC_KEY_SALT KC_FN6
/* power control of key switch board */
-#define HHKB_POWER_SAVING
+//#define HHKB_POWER_SAVING
/*
* Hardware Serial(UART)