Is your car is still exhibiting the same symptom after two VVT solenoid replacements? I presume this is the case, otherwise you’d just be crossing your fingers the second solenoid continued to do the trick. If so, then my guess is the same that Nevada above is implying, the VVT actuator is actually the problem. The solenoid is an electricity activated magnet, which creates the force needed to move the actuator into the correct position. It’s relatively easy to replace the solenoid (the electric- magnet), but considerably more difficult to replace the actuator. The VVT actuator isn’t really “inside the engine”, but it is sort of difficult to access, being hidden underneath the timing covers.
I’m not an expert on this topic btw, just offering an educated-guess diy’er opinion. Both of my vehicles predate VVT technology. VVT yields better power and improved mpg. Unfortunately that doesn’t do you much good if your car is at the shop.