Let's deal with the disappointing part first, then the useful part. There is no single best month to see a wild orangutan in Danum — and anyone who gives you one is guessing. What there is, is a factor that beats the calendar every time: fruit.
Follow the figs, not the forecast
Orangutans are walking fruit-detectors. When a stand of strangler figs comes into fruit, apes converge on it from a wide area and stay until it's stripped — and for those days, the sightings are extraordinary. When nothing local is fruiting, the same forest can feel empty of them for a week. Fig trees fruit asynchronously across the year, so there's usually something on somewhere; the skill is knowing where, and that's what your guides do every morning before you're awake.
This is why booking a stay of three or four nights matters more than picking a month. One night is a coin toss. Four nights lets the guides move you to wherever the fruit — and therefore the apes — currently is.
The near-certainty: nests
Even on a quiet week you'll see the evidence. Orangutans build a fresh sleeping nest most evenings, high in the canopy, and the old ones persist for weeks. Your guide will point out a dozen on a morning walk. It's not the same as watching a female thumb figs into her mouth while an infant clings on — but it's proof you're in occupied forest, and it sets up the moment when the real thing happens.
Mast years: the wild card
Every few years Borneo has a mast-fruiting event, when huge numbers of trees fruit at once. Wildlife activity goes through the roof — and it's genuinely unpredictable, tied to climate patterns rather than the diary. If you happen to land in one, you'll never forget it. You can't book it, so don't try; just know it exists.
So — when should you come?
Come when it suits your wider trip, stay at least three nights, and set your expectations to "very good odds, no guarantee." If orangutans are the whole point, add nights rather than chasing a month, consider pairing Danum with the Kinabatangan where riverside figs make them easier still, and read our Danum-or-Kinabatangan piece. The best-time-to-visit page covers how rain and rivers factor in. Exact fruiting-season guidance is marked as a placeholder until confirmed locally — because pretending to know is exactly the sort of thing this site won't do.