When you are calling from RingCentral but you need to Edit the Prospect or Appointment record, you'll want to open the record in a new Tab to prevent the RingCentral app from being closed or refreshed.
Each time you make a call or receive an inbound call through RingCentral, the softphone is using that webpage session. If you click Edit on the page, you are refreshing the page, closing the softphone and this will disconnect your RingCentral call.
Instead of clicking Edit on the record while you are on a Call, instead open the record you need to edit in a new browser Tab.
Simply Right-click on the record in your Recent Items menu and choose Open link in a new tab:
The Prospect record will open in a new Tab, click on the newly opened Tab:
In the RingCentral softphone you will see that you have another Call in progress on another Tab in your web browser.
From here you will be able to Edit the Prospect's information, without ending your Call.
Click View within the Softphone to see how long the call has been in progress, or to End the call.
Note: It is a best practice to set your Screen Pop settings to open a New browser window or tab when receiving an Inbound Call (rather than opening the Prospect in the same window you are working in).
Be sure when you are using the RingCentral softphone, that you are Editing and interacting with records in a different browser Tab than your phone call is taking place on. You'll want to avoid refreshing the page when a call is taking place.