  Dwarf galaxies in the Local Group appear to be stripped of their gas within
270 kpc of the host galaxy. Color-magnitude diagrams of these dwarfs, however,
show clear evidence of episodic star formation (\Delta{}t ~ a few Gyr) over
cosmic time. We present a simple model to account for this behaviour. Residual
gas within the weak gravity field of the dwarf experiences dramatic variations
in the gas cooling time around the eccentric orbit. This variation is due to
two main effects. The azimuthal compression along the orbit leads to an
increase in the gas cooling rate of ~([1+\epsilon]/[1-\epsilon])^2. The
Galaxy's ionizing field declines as 1/R^2 for R>R_disk although this reaches a
floor at R~150 kpc due to the extragalactic UV field ionizing intensity. We
predict that episodic SF is mostly characteristic of dwarfs on moderately
eccentric orbits (\epsilon>0.2) that do not come too close to the centre
(R>R_disk) and do not spend their entire orbit far away from the centre (R>200
kpc). Up to 40% of early infall dwarf spheroidals can be expected to have
already had at least one burst since the initial epoch of star formation, and
10% of these dwarf spheriodals experiencing a second burst. Such a model can
explain the timing of bursts in the Carina dwarf spheroidal and restrict the
orbit of the Fornax dwarf spheroidal. However, this model fails to explain why
some dwarfs, such as Ursa Minor, experience no burst post-infall.
