For me cutting off those long bare stems rarely worked like you'd think it would by causing them to sprout new flowering stems, but maybe I was just impatient and didn't wait long enough. However, sometimes the roots would let go when pruning showing that little root system was left even though the stems were green and leafed out on the ends. Give your's a little tug and see. Maybe it was the time of year and pruning in late summer would work. I didn't keep track of when I did it..

I'll be interested to hear what other's experiences have been.

Well, I haven't tugged on them, but I'm not terribly gentle when I grab branches to prune them (as my salvias told me today) and that one plant didn't feel loose. Plus, they've all got green leaves and are actively blooming...and have been for a few weeks. The research I've done since posting this has said to cut them back by half in late winter (one site) to encourage new growth. I haven't found anything that's Texas-related, found one that said "they only live a few years" (which isn't what I remember reading), so I have to question whether they're growing the plants in their native area.

And, the stems aren't bare right now, nothing's caused the dead leaves to drop off! :)

Mine only lived for two years. I tried cutting them back, but they didn't return for me. When you cut back, don't be tempted to do a severe cut - my experience was that Blackfoot Daisy really needed quite a bit of green left in order to rejuvenate. I had one that got woody and leggy but had new growth near the base in the spring, so I cut it back hard like I would lantana, and it just died.