At least once every month I have a vintage Airstream owner come into our shop that is convinced they need all new axle's and/or supspension. While this is definetely a good idea it's not always the case (especially if you can't afford it.) Here's what to look for: check to see if the middle of your axle is pointing toward the ground, that's not good: time for a new axle. One great way to check your axle is take it to a good tire shop and have them put your trailers axle on a micrometer, this will check to make sure the spindle is still the correct round shape.
Always, always, always replace bearings and seals if it hasn't been done recently and keep your bearings packed. I'm suprised at the amount of Airstreamers that don't do this, it's very important. I recommend doing it every spring or at the least every other year. You can also add a bearring buddy to the hub: this makes for a very simple easy way to grease your bearrings. Most axle accidents happen because of seized bearings so it's important to do this, if you don't know then you should do it to be safe.