Can you explain what it means if a manual-winding watch has "low amplitude" and what causes that? I understand that it means the watch's balance wheel doesn't rotate "enough", but why does that cause the watch to run fast? Are there any good resources for how to service manual-wind watches? (The one I have with this problem is a pocket watch)...
FWIW, it keeps time pretty well as long as I keep it wound frequently...
Got this one, Monocrom.
Low amplitude means just what you said it does -- the balance wheel isn't swinging as far as it should.
Now, a quartz watch (with a few exceptions) moves the second hand 1 time per second, right? This is why it has that distinctive jumping or ticking from second to second with a little stepping motor moving everything.
A mechanical watch moves the second hand a lot more often depending on the watch's frequency or beats per hour (bph) -- some watches 4 times (this is slow), some 5, some 6, some 8, whatever there are tradeoffs in things like accuracy and power reserve depending on the number -- this causes the "sweep". What we need to know here, is that the Balance wheel's oscillation is responsible for the bph, and, with the escapement (the thing that locks and unlocks the drive train), converting the energy in the mainspring (what you wind) into energy for everything else. As the balance wheel moves one way it releases the escapement and the second hand moves its tiny amount. Then the balance wheel gets kicked back by the escapement, swings back the other way, the escapement releases again, and the second hand moves a little further. If the balance wheel isn't getting kicked as hard as it should then isn't moving as far as it should, then it is traveling a shorter distance to each side and so it can cover the ground faster. Therefore low power = low amplitude = fast watch.
There are any number of reasons that this can happen, from bad regulation, to gunk in the system, to worn out parts. Gunk in the system -- dirt, grime, old oil -- is the most likely and a clean and oil is normally all it takes. It isn't overly hard but does require some knowledge (got this), specialized tools (don't have this), and very steady hands (really don't have this). This is a good series to get started:
http://www.clockmaker.com.au/diy_seiko_7s26/ using a watch you can get for $50 or $60, but all movements are different. It is not something you want to try 1st time on a watch you care about -- find someone who has been sitting in a dark back room hunched over so long that they can no longer stand up straight, and with a permanent squint in one eye from holding a monocle there for the past 50 years.
Finally, as far as it keeping better time if wound fully: Over the course of a single winding the watches amount of available power and speed varies. For a watch that is functioning normally when you've first wound it all the way it has a lot of power and it can't completely control the release of it so the escapement gives the balance big kicks with each pass (I've read it to be around 270 degrees to each side) so the watch is actually running slower (more ground to cover). As it releases through the center of the wind, or the largest part of the mainspring uncoiling, it runs normally. At the end it isn't getting enough power, so less kick, less swing (105 degrees), faster movement. Adjusting for this is called adjusting for isochronism, and it is more specialized than normal servicing and repair. Whether it be that your watch has to fight its way through grime or something else, it sounds like your power curve is starting in the middle and spending a lot of time at the end.
Hope I didn't lose you too early on that.