I would suspect the regulator or some restriction in the line. If you are having issues with both units, that is where I would look first. One way is to turn on a burner on the stove and watch it when you turn something on like the water heater or the furnace. If the flame gets really low when you do this, then you have a delivery problem. It could be a loose thermocouple but if you have problems with other appliances, then I would look elsewhere.
The thermocouple on older fridges provides current to keep a gas valve open. On the newer fridges, it feeds into a control board and it won't let the burn stay lit unless it senses heat. The control board shuts the burner off when the fridge is at temp and then the board opens the gas valve starts a little spark plug and ignites the flame. Dirt, wind, moisture or a bad control board can cause things not to work well.