You should be able to observe the blue flame each night, as it's the temperature of the flame and the substances burning. However, this is nature, nothing is guaranteed.
Saying that, it is reliable enough that there are tours built around it. For example, the Paket Kawah Igen Blue Fire Tour. It's in Indonesia, but running it through Google Translate, their 2 day package sounds right:
2 Day Tour Package Blue Fire Kawah Ijen Tour - Surabaya / Malang Ijen
Blue Fire Tour begins at 01:30 AM EDT up and preparation to the Post
Paltuding which is the entrance to the crater Tourism. The journey
from the inn to the Post Paltuding estimated 45 minutes, and proceed
to the location of Blue Fire Kawah Ijen by climbing or trekking around
3 km, with takes about 2 hours, attempted to arrive at the location of
the crater before sunrise, so he could see the blue flame that still
lights up. Once satisfied explore the charm and beauty of blue fire
Ijen crater and surrounding tourist, back to Paltuding and drive to
lodge / hotel for a shower and breakfast. Furthermore, check out the
hotel and went on a trip back home to Surabaya, about 18:00 pm was
already in Surabaya / poor and programs Ijen Crater Package Tour Blue
Fire ended.