I don't repitch dry yeast and rarely bother with liquid either. Since I brew 10 gallons at a time I don't brew often enough for making it worthwhile to do the whole washing/storing process.
Here's what Fermentis says about repitching - Commercially, not home brewing so much.
Recovering yeast after fermentation and repitching is possible if the cell
count is controlled to give the correct yeast pitching levels. In order to
control them, laboratory equipment will be needed. In the same way and
using the same equipment, bacteria can be removed by acid washing in
carefully controlled conditions. In case of repitching, yeast must not be
stored out of beer for long periods, even at low temperatures, as yeast
glycogen levels will fall causing slow fermentations.
Yeast mutation occurs rapidly in brewing environments, repitching can be
a delicate operation and may cause beer quality problems in terms of
flavour, yeast settling, diacetyl absorption.
Effects of repitching can be seen in as few as 3 to 5 brews especially
concerning diacetyl reabsorption. For ale beers that are generally more
flavoursome diacetyl levels are less critical.
I can tell you from experience that my Sourdough yeast cultures have dramatically morphed and changed over time and I would expect beer yeast to do the same.