What to do when Samsung Gear S is unable to receive calls?

It is the original device concept of Gear S if the calls are not forwarded to connected Mobile Device. Conversely, calls to Mobile Device can be forwarded to Gear S only when Mobile Device and Gear S are connected via Bluetooth.

If connection doesn’t establish, calls to Mobile device will ring on Mobile only.

Additionally, Gear S with Nano SIM card can work independently by stand alone mode. When disconnected from Mobile Device, Gear S can receive the calls by Gear’s itself number if Gear S’s mobile network state is Auto Switch or Always On.
 

If connected with Mobile Device, Gear S can receive the calls by Gear’s itself number only on Always On state. If Gear S’s mobile network is Auto Switch while connecting to Mobile Device , Gear S will turn off the modem for enhancement of Gear S usage time. As a result, Gear S can’t receive the call or message on Gear.