What you are describing sounds strictly like an issue on your laptop installation. You should be able to seamlessly be logged into both your mobile phone Webex App and your laptop Webex App, using either device to respond to messages or answer calls throughout your workday. Are you saying this never occurs if you use ONLY the laptop for a day? Does the Webex App have issues after some time, or after stepping away and unlocking the machine after a period of inactivity?
I would suggest to uninstall/re-install and see if the issue persists, if you have not already, as a starting point.