Hi there,
So I don’t think the C3 supports Lite-Sleep. AFAIK that would be needed to keep the radio ON,
like the S3, or Nrf52840 does in those cases. The C6 I believe allows a ULP connection but super low Sleep current.
What about just advertising the data, without a connection? just a thought?
Check the C3 data-sheet and be sure you are able to do what your thinking sleep wise, and are you using the BLE connection callbacks in your code? if so you may need to add a STUB or modify what you have so upon waking it doesn’t reset, just reconnects.
HTH
GL 
PJ 