OK. I figured out the problem by looking at the lens parameters, like Jim Watters suggested.
When I drag an image taken directly from my Ricoh Theta M15 camera, onto Hugin, and select "Equirectangular" projection, the lens horizontal field of view (HFOV) gets automatically set to 369.5 degrees. But the HFOV value should be 360 degrees. So the stitch ends up discarding part of my original image.
On the other hand, when I drag an image that I resized onto Hugin, a dialog pops up ASKING me what the HFOV is, so I type "360" and all works OK. Presumably some metadata has been discarded from my resized image.
Obviously, the workaround is to always manually set the HFOV to 360. The perfect world solution would be for either a) the Ricoh Theta M15 to write metadata that does not confuse Hugin, or b) for Hugin to not be confused by the metadata that the Ricoh Theta M15 writes.
Thanks Cartolo and Jim for your help.