The number I hear is that tandem sales are about 1% of bicycle sales. I don't know if this has varied historically. In the on topic era, there were several key areas that failed with some regularity on tandems. The big 2 for me were freewheel failures and rear wheel spoke breakage. Old Santana tandems had a very nice spoke holder on the driveside chainstay. Although I never had to try it, getting a freewheel off out on the road could not have been a lot of fun as they were torqued on pretty tight. The stoker compartments were also much shorter than current designs, making stokers intimately familiar with their captains' asses. I still have flashbacks to a Montauk century I did around 1983 as a stoker!
While current tandems are much more dependable, they are still expensive and hard to transport and take up a lot of room. For urbanites, they don't fit into many elevators (or apartments) and are not fun to carry up stairs.
Still, I'm doing my part to keep them going, currently owning 4. The 1979 Claud Butler I bought from a friend's estate did TOSRV twice and someday I'll get it in shape to ride again. It has a custom modified Campagnolo NR brake lever that controls 2 brake cables and a Phil Wood disc brake that Harvey Sachs has reminded me is unsafe.
Len Diamond
Ridgewood, New Jersey USA