  The Mira variable R Hydrae is well known for its declining period, which Wood
& Zarro (1981) attributed to a possible recent thermal pulse. Here we
investigate the long-term period evolution, covering 340 years, going back to
its discovery in AD 1662. Wavelets are used to determine both the period and
semi-amplitude. We show that the period decreased linearly between 1770 and
1950; since 1950 the period has stabilized at 385 days. The semi-amplitude
closely follows the period evolution. Detailed analysis of the oldest data
shows that before 1770 the period was about 495 days. We find no evidence for
an increasing period during this time as found by Wood & Zarro. IRAS data shows
that the mass loss dropped dramatically around AD 1750. The decline agrees with
the mass-loss formalism from Vassiliadis & Wood, but is much larger than
predicted by the Bloecker mass-loss law. An outer detached IRAS shell suggests
that R Hya has experienced such mass-loss interruptions before. The period
evolution can be explained by a thermal pulse occuring around AD 1600, or by an
non-linear instability leading to an internal relaxation of the stellar
structure. The elapsed time between the mass-loss decline giving rise to the
outer detached shell, and the recent event, of approximately 5000 yr suggests
that only one of these events could be due to a thermal pulse. Further
monitoring of R Hya is recommended, as both models make strong predictions for
the future period evolution. R Hya-type events, on time scales of 10^2-10^3 yr,
could provide part of the explanation for the rings seen around some AGB and
post-AGB stars.
