Your heater being original could very well mean that the air intake vent (behind the grill that's in the top left corner of the lid you open to light it) has rusted out internally.
We had exactly the same problem as you; if the wind came onto the streetside of the TT, we could pretty much count on either going out every while to re-light, or not having hot water until the wind died.
We tried cutting a tin can (from a can of peas) with a notch so it would slide over the section where the pilot is, and that seemed to help a bit, but it wasn't perfect.
We finally wound up replacing the water heater, since it sprung a bad leak and was wetting the carpet in the bathroom. The new one we bought has not had any use, but I did note in looking at it that the door fits much more snugly over the entire face of the heater. And, of course, the air intake louvre is not rusted at all.
We won't know until next year if that fixed the problem or not, but I do suspect it will.
Camping World has the 10 gallon Atwood on at $399 now, and the 6 gallon at $349, if you get tired of re-lighting.
That's for the manual one, there are more automated ones for more $$...
If you replace it, don't forget to install a bypass if you don't already have one.