No.

It depends on the context.

When followed by a parenthetical phrase —yes.

'Winnie is arguably the best-dressed girl in the school. But, on a number of occasions, Hortense has deserved this accolade'.

I totally agree with the above answer. The only reason a teacher may give you a hard time, however, is if you're taking a class on writing fundamentals. In composition courses, it is generally frowned down upon to begin your sentence with a conjunction.

The second comma is necessary in your sentence. The first serves to indicate a pause, but commas are not used for indicating pauses. "On a number of occasions" is an introductory prepositional phrase and should have a comma after it. It is possible that the phrase is an interruption. If that is the case, the comma still has nothing to do with "but."

There should not be a comma after "but.

Englishmaven "On a number of occasions" is an introductory prepositional phrase and should have a comma after it.

I was told 'no' by my dissertation adviser. Personally, sometimes I use a comma with those prepositional phrases, and sometimes I don't.