How often is QFE set on an altimeter during flight?
You don't use QFE or QNH in an airspace, you use it for a purpose. 

QFE is rarely used in the US, other places in the world it's primarily used for landing, although that's personal preference (I use QNH). You set QNH on the ground at your departure airfield using the local setting then update QNH on route, when approaching an airfield for a landing you would use that airfield's QNH setting as given to you over the radio or from an information broadcast. 

The only time I could see setting QFE more than once would be in the case of a diversion, if you needed to fly to another airfield you'd need to go back to QNH, then set the local QFE at the other airfield. This is extra workload and could be a forgotten step, which one of the reasons I prefer QNH for landing - it's one less thing to do.