Diagnosis
No, it should be firm. The barrel is likely not fully and correctly seated onto the base's drive shaft.
How to Fix It
Unplug the device. Firmly pull the entire rotating barrel straight up to remove it. Inspect the square plastic drive shaft on the base and the corresponding socket in the barrel for any debris. Align the shapes and push the barrel straight down until you feel and hear a definitive click. It should now feel secure.
If That Didn't Work
The plastic retention clip inside the barrel socket that holds it to the shaft may be broken. This causes permanent wobble and requires a new barrel.
Heads Up
Always store it upright. Laying it on its side can put pressure on this connection and weaken it over time.