Why does the pH of this solution rise instead of fall when exposed to the atmosphere?
At that pH, you're well outside the buffering capacity of both phosphate and boric acid, so a $\mathrm{pH}$ rise from $5.5$ to $5.9$ corresponds to a net increase in base of about $2\ \mathrm{\mu M}$.  That implies to me that it's likely something going on with one of the first five ingredients in your recipe, or the $\ce{HCl}$ added to adjust the $\mathrm{pH}$.

I can think of two scenarios:


Similar to Brinn's answer, perhaps a small amount of $\ce{HCl}$ has evaporated out of solution.
If your $\ce{Fe-EDTA}$ was added as $\ce{Fe(II)-EDTA}$, oxidation to $\ce{Fe(III)-EDTA}$ could explain the pH rise, by reducing water to hydrogen gas and hydroxide ion:


  $2\ \ce{Fe(II)-EDTA} \rightarrow 2\ \ce{Fe(III)-EDTA} + 2\ e^-$
  
  $2\ \ce{H2O} + 2\ e^- \rightarrow \ce{H2} + 2\ \ce{OH-}$



I don't know offhand how thermodynamically or kinetically feasible #2 is.  With all of the other metals present in solution, though, it's not unreasonable to imagine that some sort of catalysis might be possible.