  Recent hydrodynamical simulations predict that stellar feedback in
intermediate mass galaxies (IMGs) can drive strong fluctuations in structure
(e.g., half-light radius, $R_e$). This process operates on timescales of only a
few hundred Myr and persists even at late cosmic times. One prediction of this
quasi-periodic, galactic-scale "breathing" is an $anti$-correlation between
star formation rate (SFR) and half-light radius as central gas overdensities
lead to starbursts whose feedback drags stars to larger radii while star
formation dwindles. We test this prediction with a sample of 322 $isolated$
IMGs with stellar masses of $10^{9.0} \leq M/M_{\odot} \leq 10^{9.5}$ at
$0.3<z<0.4$ in the HST $I_{814}$ COSMOS footprint. We find that IMGs with
higher specific SFRs (SSFR $>10^{-10}$ yr$^{-1}$) are the most extended with
median sizes of $R_e \sim 3-3.4$ kpc and are mostly disk-dominated systems. In
contrast, IMGs with lower SSFRs ($<10^{-10}$ yr$^{-1}$) are a factor of $\sim
2-3$ more compact with median sizes of $R_e \sim 0.9-1.6$ kpc and have more
significant bulge contributions to their light. These observed trends are
opposite the predictions for stellar feedback that operate via the "breathing"
process described above. We discuss various paths to reconcile the observations
and simulations, all of which likely require a different implementation of
stellar feedback in IMGs that drastically changes their predicted formation
history.
