Local conditions will strongly influence this so it's impossible to give a reliable answer, but certainly you should be able to get more than one season from something like this regardless of the weather conditions. Even completely unprotected and exposed to plenty of wet weather pine won't rot away in just a year or two, although the laths are very thin so you should probably expect some warping and cracks or splits.
Possibly the weakest aspect of the construction of these is actually the staples, they may well fail first if they get rusty and the conditions are damp enough for the rust to progress.