The announcement states that the conference's governing body, the European Cycling Federation (ECF), sent notice of the rejection to the cycling club by post but included no explanation. Neither did the notice say which city, if any, has won the bid. The club was going to write a letter to ECF seeking an explanation.
My colleague Daniel Mourek, who's active in ECF, said he hadn't heard the news, but noted that the host for any Velo-City conference must guarantee a substantial investment into the conference (more than EUR 400,000, I believe), and this MAY have been an obstacle for Budapest. But this was just conjecture.
From what Mourek's heard, the only other candidate city for this conference at this time was Seville.
I've written to ECF's secretary general in Brussels, Bernhard Ensink, for some insights. If I get a reply, I'll pass it on.