score:6
Per the official site, trains run three times a day, every day of the year (毎日運転). However, there are a few periods when some runs of the special train with wood paneling and panorama windows etc are replaced by an 'ordinary' express:
Do note that while all three trains run from Fukuoka (Hakata) to Yufuin, the Yufuin-Beppu bit of the route is served only once per day by Nr. 3/4.
Re: pricing, my understanding is that all seats are the same price, and the panorama section is open to all.