Intermittent low pressure natural gas to outside grill
As you can see from the image natural gas is supplied to commercial industrial and residential customers off the same line. I know it's a crude image but it's really how it works. If there was a significant pressure drop on a main branch of the system then commercial and industrial customers would be offline, resulting in Factory shutting down and other complications.  Residential draw is the equivalent of taking a cup out of a swimming pool. That being said I would replace the regulator. I have been on the receiving end of some really nice barbeques because of faulty regulators. I actually have a bin of them right next to me as I write this.  it's the one marked REGS it's an inexpensive repair. The only other thing I would look at is the gas line in your house. If it's undersized and your furnace or water heater starts you could experience pressure drop, resulting in a lazy flame.