Sorry - forgot to include the screen capture:

I thinks there'a a problem with your blue part.

Beside that , bodies with knife edges may not behave properly - usually, something like you have depicted, would be designed in 4 duplicated segments - although you may not start off that way, anything can be done later as your design intent emerges ( becomes apparant ) as progress is made.

Bodies can't be joined at knife edges...

but can be joined if A) overlapping...

or B), coincident face.

Hope this helps...

Solids can not be joined if they share the same edge. There is nothing to join to. Overlap them slightly, even by a fraction of a millimetre so you have two surfaces however small they are will be joined.

If you do not want to, or can't overlap the edges then draw something small so the solids will combine.

Thanks all.

The blue solid is 1.030" diameter at the widest part, with a 0.7" square (plus odd bits away from the corners) opening, so the four apparent elements are actually connected if you zoom in in the program. (I have the object set to partly transparent, which is why the corners 0.02" in from the outer circumference look like they are breaking through in the screen capture.) And geometry checks on each of the two solids reported no problems.

My reason for needing to combine them into a single solid has gone away. But I'll do some experimenting when I have some free time to try isolating the cause.

So the blue part is already one solid and you want to join it to the brown solid?

Select each end in turn of the brown solid and 'Move' each away from the blue solid. Now use the 'Pull' tool on each end and pull 'Upto' the blue solid. This will make sure the ends will be exactly the same curve and shape as the blue solid. If that does not work then 'Move' each end into the blue solid.

Thanks Jacant (and others who responded),

As evidenced in the structure tree in the screen capture I had posted, there were just two solids present, the blue one and the brown one.

Jacant's method worked.

I was a little surprised that DS Mech didn't see at least one of pair of faces as coincident to begin with, as I had drawn the brown solid's elements based on points on the blue solid, then extruded (with the blue solid hidden to prevent merging originally). The elements of the brown solid are just intended as a bed adhesion aid during 3D printing, which I snip off afterward.
Conceptually it made sense to make it as two solids, one the "keep" part, the other the printing aid.