I'm hoping to write some informal posts to this forum addressing the value of visual observations in LPV research, and the need for continued visual monitoring of LPVs and other long-observed targets in the AAVSO observing program. In March of 2010 we started a conversation on historical trends in visual observing  on aavso-discussion, particularly on the declining numbers of visual observations submitted to the AAVSO and the reasons for the decline. A number of different issues were raised in that discussion, and I hope to address many of them with posts to this forum. Today I want to preface that discussion by very briefly talking about two basic uses for long-term visual light curves in variable star research.
The longest and most homogeneous data sets for variable stars come from visual observers. Some stars have visual light curves spanning multiple centuries, but the majority of AAVSO visual light curves span from 50 to 100 years in length. In general, visual data sets for stars with good sequences are capable of tracking long-term changes of a few tenths of a magnitude over time, and are capable of detecting periodic behavior with amplitudes as low as 0.05 magnitudes. Both of these are important and valuable measurements in studying astrophysical processes that occur on long timescales.
First, LPV stars are "rapidly evolving" in the cosmic sense; changes can occur on timescales measurable in less than a human lifetime -- years or decades. These changes may include changes in mean light, period, amplitude, or light curve shape, and the appearance or disappearance of different pulsation modes. Such changes can and often do involve photometric variations of more than a few tenths of a magnitude which visual observers are more than capable of following. Any star that is correctly classified as a Mira or semi-regular variable can be followed by visual observers, and those observations will have use both in the present and in the long term. More importantly, the longer these data sets become, the more valuable they are. As the length of all of our LPV light curves grow, the more likely it is that we will detect stars undergoing long-term changes in behavior. It's impossible to predict which stars will show this, but we can predict that it will happen to some of them, if we keep watching. And LPVs aren't the only stars where this matters. Several classes of variables can show long-term changes including the R CrB stars, dwarf novae and other cataclysmic variables, symbiotic stars, and many classes of young stellar objects like T Tauri stars.
Second, when stars are strictly periodic, one can extract signals from data with large scatter, sometimes even when the scatter of individual points is larger than the signal itself. If a sufficient amount of data exist with homogeneous statistical properties, you can often use straightforward statistical techniques to extract a signal. The reason is that true "noise" will introduce random changes in a measurement, while a true signal will always push the measurement in one direction or another. Given enough measurements collected over time, the signal will begin to dominate the noise. The resulting values for periods, amplitudes, and phases will be limited by the amount of scatter in the data and the amount of data available. Instrumental data are currently the preferred means for measuring precise timings of individual maxmima (Cepheids, RR Lyrae, and delta Scuti stars) and minima (EBs). However, in the absence of instrumental data, visual data can also certainly fill in gaps in instrumental coverage over long periods of time if the precision of the derived timings is sufficient to constrain trends in maxima and minima timings.
One of the things that constrains the usefulness of visual data is that they have to be homogeneous in a statistical sense: either the data have to come from one observer who makes a consistent and unbiased measurement over long periods of time, or they have to come from a collection of observers whose statistical properties don't change over time. The latter is a reasonable assumption to make for a large number of observers all working from similar sequences and observing in a similar fashion. Most visual observers use one of a small number of techniques to measure the brightness of variables, and most visual observers have ocular acuity and sensitivity within a range typical of human eyesight. Given a sufficiently large number of observers and a sufficiently long span of observations, visual light curves have well-understood statistical properties and can be analyzed using normal statistical methods just like any instrumental data set.
For each of the years 2000 to 2009, the AAVSO received observations of between 4000 and 4800 individual stars, including LPVs, cataclysmic variables, and others; about 25 percent of these stars received more than 50 observations in a given year, averaging about one observation every week. That's just about the bare minimum coverage to adequately cover something like a Mira variable with a period less than a year. Some stars have excellent coverage, while some are quite poorly observed. For many stars in the AAVSO program, the number of visual observers and observations remains sufficient to allow researchers to treat them like any other data set; there remains good astrophysics to be done using these long-term light curves.
However, this will only remain true if a sufficient number of people continue to observe them; in 2010 we received visual observations for 3712 stars, of which only 760 were observed more than 50 times. The total number of visual observations submitted in 2010 (163400) is just over 1/3 of the number submitted in 1995 (385500), our peak year for visual observing. We are seeing a clear decline in the number of visual observations submitted to the AAVSO per year, along with a measurable but less dramatic decline in the number of visual observers and the amount they observe. Interestingly, the total number of visual observers is not dramatically lower, although the number of observers who contribute more than 100 visual observations per year is about 2/3 of what it was in 1995.
We hope to turn these numbers around in 2011 by providing better guidance to visual observers on what targets to select, as well as better justification of why your visual observations matter. But to summarize all of this discussion as succinctly as possible:
If you're a visual observer, please keep observing! It matters!