I am using parts of the ANCS example code within a product near pre-production. I am able to reproduce the problem in the ANCS example without modification. Here are the specifics:
ANCS example fails with error "NRF_ERROR_NO_MEM" within nrf_sdh.c, "SD_EVT_IRQHandler". The SDK is 15.3.0 and the SoftDevice is s132_nrf52_6.1.1_softdevice.hex.
This is easily reproduced with the following steps:
1) Have an iPhone with 30 or so text message notifications uncleared (text message icon shows red 30 number on icon);
2) Start ANCS;
3) Pair iPhone to Nordic Semiconductor ANCS example;
4) Turn Bluetooth off;
5) Turn Bluetooth on;
Upon reconnection this error will be reproduced.