Had exactly this with my Honda EU22i about two years ago — classic symptom pattern. The 20-minute window is the giveaway; that's roughly how long it takes for the engine to reach full thermal equilibrium.
Worth working through these in order before condemning the AVR:
1. Fuel delivery
Carburettor needle jet partially blocked. Heat causes fuel to vaporise unevenly once the carb body gets hot. Clean it properly with an ultrasonic cleaner if you can.
2. Low oil shutdown
If the oil level is even slightly marginal, the thermal expansion of everything internal can trigger the low-oil sensor prematurely. Top it up and test.
3. Capacitor on the AVR itself
On Chinese inverter-generators (Kipor, Hyundai, etc.) the capacitor on the AVR board degrades with age and heat. Costs pennies to replace but you need to match the µF rating exactly.
4. Cooling/airflow
Are you running it in an enclosure or somewhere restricted? Generators need proper airflow — surprising how many people box them in thinking they're being clever about noise.
What generator model are you actually running? That'll narrow it down considerably. Also — is it cutting out completely (engine stops) or just losing load (engine keeps running but output drops)? Those are two very different fault trees.
If the engine is stopping, I'd bet on thermal protection or fuel starvation before touching the AVR. If output drops but the engine runs on, then the AVR or capacitor becomes more likely.
Happy to help diagnose further if you can share more details.