  The availability of a large amount of observational data recently collected
from magnetar outbursts is now calling for a complete theoretical study of
outburst characteristics. In this letter (the first of a series dedicated to
model magnetar outbursts), we tackle the long-standing open issue of whether or
not short bursts and glitches are always connected to long-term radiative
outbursts. We show that the recent detection of short bursts and glitches
seemingly unconnected to outbursts is only misleading our understanding of
these events. We show that, in the framework of the starquake model, neutrino
emission processes in the magnetar crust limit the temperature, and therefore
the luminosity. This natural limit to the maximum luminosity makes outbursts
associated with bright persistent magnetars barely detectable. These events are
simply seen as a small luminosity increase over the already bright quiescent
state, followed by a fast return to quiescence. In particular, this is the case
for 1RXS J1708-4009, 1E 1841-045, SGR 1806-20, and other bright persistent
magnetars. On the other hand, a similar event (with the same energetics) in a
fainter source will drive a more extreme luminosity variation and longer
cooling time, as for sources such as XTE J1810-197, 1E 1547-5408 and SGR
1627-41. We conclude that the non-detection of large radiative outbursts in
connection with glitches and bursts from bright persistent magnetars is not
surprising per se, nor it needs of any revision on the glitches and burst
mechanisms as explained by current theoretical models.
