  Several theories exist to explain the source of the bright, millisecond
duration pulses known as fast radio bursts (FRBs). If the progenitors of FRBs
are non-cataclysmic, such as giant pulses from pulsars, pulsar-planet binaries,
or magnetar flares, FRB emission may be seen to repeat. We have undertaken a
survey of the fields of eight known FRBs from the High Time Resolution Universe
survey to search for repeating pulses. Although no repeat pulses were detected
the survey yielded the detection of a new FRB, described in Petroff et al.
(2015a). From our observations we rule out periodic repeating sources with
periods P $\leq$ 8.6 hours and rule out sources with periods 8.6 < P < 21 hours
at the 90% confidence level. At P $\geq$ 21 hours our limits fall off as ~1/P.
Dedicated and persistent observations of FRB source fields are needed to rule
out repetition on longer timescales, a task well-suited to next generation
wide-field transient detectors.
