Not all Tolumnia send out new spikes, but some do. It's a bit less common in hybrids than species. Trimming dead sections for esthetic reasons causes no harm.
Thanks for this pic. I bought 4 at a show in January. They are beautiful, one just finished blooming and the other 3 are in full bloom. I was admiring them last night with a clippers in my hand ready to cut off the old stalk, when I remembered someone saying they (can) sometimes rebloom. I didn't cut it, now I see they can really re-bloom. Thanks