[mrsmith]

I’m not saying there are no exceptions at all, but it seems a necessary and regular procedure- not weird at all.
Search it and there are numerous examples.

[Cboldt]

I have searched it, many times. Reconsideration under cloture wasn't common until maybe 6-8 years ago. Not tooting my own horn, but see this link for evidence that I followed the senate fairly closely for a few years.

It (reconsideration of a failed cloture motion) is not necessary, and it is weird. If a cloture motion fails, the subject is still alive. Just file another cloture motion, they are free. I can point to numerous examples where cloture was attempted multiple times on a single subject. See Bush judicial nominees.