A mini-split removes moisture by condensing it on a cold coil. That requires the coil to be cold and the air to keep passing over it, which requires the unit to keep running.
The four causes, in order of likelihood
The head is oversized. It reaches setpoint quickly and turns down to minimum or stops. Short run time means little moisture removed. This is by far the most common cause and it is designed in at installation.
The fan is set too high. High airflow across the coil means the coil runs warmer and condenses less. Auto or low fan dehumidifies better than high.
The setpoint is too low. Counterintuitively, setting 68°F rather than 74°F can make a room feel worse, because the unit reaches the low setpoint fast, stops, and leaves the humidity behind.
The load is mostly latent. A basement, a bathroom-adjacent room, or a house with a damp crawl space has a moisture load the cooling equipment was never sized for.
Dry mode
Most ductless heads have a dry or dehumidify mode. It runs the compressor with a low fan speed and cycles to hold humidity rather than temperature.
It works, with two caveats: it does not control temperature closely, and on many units it has limited capacity. It is a useful tool on a mild damp day and it is not a substitute for correct sizing.
What to measure
Indoor relative humidity, with a cheap hygrometer. Comfortable is roughly 45–50% in summer. Above 55% while the temperature is being held is the confirmation.
Run time. On a hot afternoon a correctly sized head runs continuously at low output. If it reaches setpoint in ten minutes and stops, it is too large for the room.
What can be done without replacing anything
Lower the fan speed to auto or low. The single easiest change and it frequently helps.
Raise the setpoint a degree or two, which lengthens run time.
Use dry mode on humid days.
Reduce the moisture source — bathroom and kitchen exhaust that actually vents outside, a sealed crawl space, gutters that discharge away from the foundation.
Add a standalone dehumidifier in the worst room, which addresses the latent load directly and is much cheaper than changing the equipment.
If the head really is too large
Replacing a head with a smaller one on an existing multi-zone system is sometimes possible within the connection ratio, and it is worth asking about rather than assuming the whole system has to change.
On a single-zone system both the head and the condenser are matched, so it is a fuller replacement.
Either way, the calculation to do first is a proper room load, because the same error made twice produces the same complaint.
The design lesson
Ductless equipment modulates, which makes people relaxed about sizing. The modulation range has a floor, and a head two sizes too large spends the season below that floor.
Sizing to a room load calculation rather than to a generous rule of thumb is what avoids the whole problem, and it is a short calculation for a single room.
Winter is different
In heating mode the same equipment adds no moisture and the air dries out, which in a very tight house can go too far the other way.
That is a humidifier question rather than a mini-split question, and it is worth separating the two seasons when describing a complaint to a contractor.
The condensate is the evidence
A head that is dehumidifying produces water, and that water leaves through the condensate line.
If the drain is dry on a humid day while the unit is running, it is not condensing anything, and the diagnosis above applies. If the drain is running steadily and the room still feels damp, the moisture load is larger than the equipment can handle and the source is worth finding.
That is a thirty-second check that separates the two cases.