Nisaa
Yes. Istihadah does not stop a woman's fast, in the same way it does not stop her prayer. She continues fasting for as long as the irregular bleeding lasts, taking the same precautions against soiling and the same wudu-before-each-prayer routine that governs her prayer during istihadah.
The reasoning starts with what istihadah actually is. The Prophet (Salla Allahu 'Alayhi Wa Sallam) told Fatimah bint Abi Hubaysh (Radi'Allahu Anha), who asked him whether she should abandon prayer: "No, that is from a vein and not menstruation." (Narrated by al-Bukhari and Muslim). Because istihadah is not classed as hayd, it does not carry hayd's rulings, and fasting is only suspended for hayd and nifas specifically. 'Aishah (Radi'Allahu Anha) said: "When we would have our menses during the lifetime of the Prophet (Salla Allahu 'Alayhi Wa Sallam), we were ordered to make up the days of fasting that we had missed." (Narrated by al-Bukhari). That instruction is tied to menstrual bleeding, and istihadah does not meet that description.
There is also a stronger case sitting right next to it. Janabah, a major ritual impurity, does not invalidate a fast even when it persists past Fajr, because it only obliges purification before the next prayer, not before the fast can continue. Istihadah is treated as a lesser, continuous minor hadath, comparable to chronic incontinence, not a major impurity at all. If Janabah leaves the fast untouched, istihadah, which asks less of her than Janabah does, cannot reasonably be read as stopping it either. The four madhabs are agreed on the result: fasting continues.
What actually changes for her fast
Nothing about the fast itself. She eats suhoor, forms her intention, and fasts the day normally. The adjustments istihadah asks for belong to her prayer, not her fast:
- A pad or cloth, to guard against soiling her clothing and the prayer space, the same precaution described in the hadith of Hamnah bint Jahsh (Radi'Allahu Anha) (Narrated by Abu Dawud and al-Tirmidhi).
- Wudu before each prayer, renewed at every prayer time rather than carried over, on the position the majority of scholars across all four madhabs act on.
Neither of these has anything to do with whether the fast is valid. Wudu is a condition for prayer, not for fasting, so there is no wudu-equivalent requirement standing between istihadah and a valid fast.
Why this is worth confirming for yourself
Istihadah is only istihadah once it is told apart from hayd, by its colour, thickness and timing against your known cycle. If what you are bleeding matches the characteristics of menstrual blood or falls inside your normal cycle length, your fast is invalidated the moment it starts, and that day is made up afterward, the same as any other day of hayd in Ramadan. Getting that classification right first is what decides which of these two rulings actually applies to you.