How can I ensure portable generator success during a long natural disaster?
I live in southern New England, where we can usually see our natural disasters coming a few days in advance (snowstorms, hurricanes, etc.), so your considerations will be different, but I'll share what I do and what I've learned in three 5+ day outages over the past two years; it may give you some reference points.

Fuel reserves

I have a gasoline-powered generator, rated for 7000 watts, enough to run our well pump, two furnaces, refrigeration and some convenience items (not all at once, we have to manage around the well load if the furnaces are being run).  I test-run the generator about once a month, running it for about ten minutes.   I keep the tank nearly empty so that when I add fresh gas there won't be a lot of old gas mixed with it.  I add preservative to all my gas when I buy it.

I adjust my fuel reserves by season -- more in the winter when an outage could turn from an inconvenience and spoiled food to property damage from frozen pipes.   When an event is predicted, I max out my portable containers (about 12 gallons) and top off my truck (23 gallon tank).  I have a siphon hose that can reach the bottom of the truck's tank, and have tested using it.   Depending on the season, we can burn 3-6 gallons a day, so this sets us up for 4-5 days (assuming that I can get half the fuel from the truck tank).  If the event doesn't materialize, I burn the gas off in the truck before it sits too long.

I built a rain cover for our generator so that it can be run in rain or snow.   It takes a few minutes to install, I sometimes do this pre-event so we can roll it out and fire it up on short notice.  I also test run right before a possible event.

Spare parts

I keep oil, a spark plug, and some fuel line handy, the plug is clearly marked "Generator".   I had a leaky fuel line once when I needed the generator, thus the spare fuel line on hand.

Other

Make sure you know how to start the generator manually; electric start systems may or may not be there when you need them.  I use a battery maintainer (a trickle charger with intelligence to prevent overcharging) and I make sure the battery is fully charged after each test run.

Use

Plan for what you will want to use, and make sure you have a way to get power from the generator to the loads you want to power.   We have a transfer panel that supplies the well, furnaces, fridge, freezer, convenience outlets in the kitchen, and lights in the powder room and central stairway (this turned out to be genius, as the stairway lights cover a large part of our open floor plan house).   I relocated the power supply for our alarm system to the same circuit as the freezer after killing off the system's battery during our first extended outage.  I also put put a table lamp on the freezer circuit so there's light in the garage (no windows) when the generator is running.

We've run extension cords for the TV &amp; Satellite dish from the nearby kitchen, to the basement for the DSL modem and router (amazingly, we had internet through most of our outages).   We charge phones, laptops, etc., in the kitchen when the generator is running.

We have a pond with fish in it; I put a 15-watt aerator in with an extension cord in warm weather instead of running the 600 watt pump that normally power its waterfall.

We have a rechargeable lantern that we use for bedtime, trips outside, etc. and recharge it during the day; a gas grill and coleman stove cover our cooking (we can relocate our microwave near a generator outlet if needed, but haven't done that yet).   The coleman stove is great for heating water (we have electric hot water and range) as well as general cooking.

We do not run the generator full time; typically run it about 1/3 time (typically running it until the refrigerator compressor cycles off), but it varies based on our expectation for length of outage/fuel reserves, desire to have the TV, etc.

Our generator doesn't automatically charge its own battery; rather than using the unregulated (I think) battery charging cable provided with it, I use the battery maintainer plugged into one of the outlets on the generator.

After the last long outage, I bought a 150 watt inverter with the idea that it could be used to power some LED lights and a radio when we have the generator off, using a battery borrowed from a golf bag cart; this hasn't been tried yet, though.