I didn’t think there was specific reason courts would rule against it, but sometimes people get real creative when they challenge things in court.
I was pretty sure this was the case - "Each House may determine the rules of its proceedings, punish its members for disorderly behavior, and, with the concurrence of two thirds, expel a member. " So the filibuster falls under “rules of proceedings” (Article I, section 5)
Which means that filibustering (or not) passes constitutional muster, as a procedure to be determined by the legislative body, not something for the court to rule on.
I think I can guarantee without any likely cavil that the filibuster is fully constitutional:
“Each House may determine the Rules of its Proceedings…” (Article I, Section 5, paragraph 2). If the House formally required in its Rules that anybody testifying before one of its committees wear a ballet tutu, a red clown nose, and prefix his/her remarks with “Wooba, wooba, wooba,” that would be completely constitutional.
ETA: “Damn you, Bijou Drains!!!” 
Hmmm. It would certainly make C-SPAN more interesting.
In fact, we ought to pass an amendment requiring that. I don’t want anyone making policy decisions who’s afraid of a little good-natured public humiliation.
Just to clarify, the “nuclear option” being discussed a while back in the context of cloture was not the cloture vote; rather, it was the effort to rewrite Senate rules to do away with the need for a supermajority cloture vote, reducing the required votes to a bare majority.
Good point – the metaphor has taken on such a life of its own that I wasn’t even thinking where it first was (metaphorically) used! :o
Are there any numbers available for the frequency with which it has been used in recent years?
no not necessary. if no compromise is reached the the bill might not come up for discussion, or before bringing it up for discussion the senate can vote to limit the amount of time each senator can hold the floor.