  The accretion-powered millisecond pulsar IGR J00291+5934 underwent two ~10 d
long outbursts during 2008, separated by 30 d in quiescence. Such a short
quiescent period between outbursts has never been seen before from a neutron
star X-ray transient. X-ray pulsations at the 599 Hz spin frequency are
detected throughout both outbursts. For the first time, we derive a pulse phase
model that connects two outbursts, providing a long baseline for spin frequency
measurement. Comparison with the frequency measured during the 2004 outburst of
this source gives a spin-down during quiescence of -4(1)x10^-15 Hz/s,
approximately an order of magnitude larger than the long-term spin-down
observed in the 401 Hz accretion-powered pulsar SAX J1808.4-3658. If this
spin-down is due to magnetic dipole radiation, it requires a 2x10^8 G field
strength, and its high spin-down luminosity may be detectable with the Fermi
Large Area Telescope. Alternatively, this large spin-down could be produced by
gravitational wave emission from a fractional mass quadrupole moment of Q/I =
1x10^{-9}. The rapid succession of the outbursts also provides a unique test of
models for accretion in low-mass X-ray binaries. Disk instability models
generally predict that an outburst will leave the accretion disk too depleted
to fuel a second outburst after such a brief quiescence. We suggest a
modification in which the outburst is shut off by the onset of a propeller
effect before the disk is depleted. This model can explain the short quiescence
and the unusually slow rise of the light curve of the second 2008 outburst.
