Very occasionally my chain will come of the small chainwheel on a downshift. It is not at all predictable, except that it always happens when the I'm doing an unloaded shift in preparation for a climb. I don't think it has ever happened under load.
The limit screws seem to be set correctly. Most (>99%) of the time I can shift onto the small chain ring without any problem – both under load and without a load.
I'd appreciate suggestions for what to check or ideas about what could be causing this.
From the way you describe the problem it seems less likely to be one of the common mechanical causes, like a stiff chain link or bent chainring. I have two guesses as to the cause. One is a subtle mechanical problem that requires the right conditions to set it off. The other is about technique.
The rear derailleur may not be taking up enough slack when you're in the small chainring. (This is not always obvious.) If you happen to shift around the time you hit a little bump or dip, or while you throw your weight forward to stand, or while you adjust your cadence, the slack chain gives a bounce and off it comes.
You may be shifting improperly on these rare occasions. If you shift to the innermost chainring while you're in the outermost cog, and the chain line is angled too sharply, off it goes. Also, to reduce the odds of dropping the chain, a front shift ought to be done like this.
I would just tweak the limit screw for the low side a bit. See if the problem goes away and you can shift into the low chain ring reliably. Occasional problems are hard.
I've experienced this problem when the small chainring has one lose bolt, so check for that, and also that the chainring is perfectly flat. Note that prolonged use of a chainring with lose or missing bolts may result in bending it.
A wobbly chainring wont have a uniform distance from frame's centerline, thus, it won't have a regular position relative to the front derailleur. In my cases, the same can happen between large and middle chainring too, but is perceived only as "difficult shifting" rather than chaindrop.
This could explain why it happens only some times, because you wont initiate shifts always in the same rotational position of the crank. (e.g. sometimes you shift when right foot is up, some times the opposite)
Another cause for wobble could be a lose crankset or a faulty bottom bracket, although these two are more rare. I've experienced both problems on, admittedly, extremely neglected bikes. A loose crankset on a square taper spindle, that luckily was properly tightened before permanent damage was done, and a poorly sealed BB cartridge that ended in catastrophic failure (should have replaced it way sooner).
Large chainring shift to small chain ring while chain is in largest rear cog = chain drop
