DIAGNOSIS This is typically a sensor issue. The cliff sensors (usually four, on the underside) are getting "phantom" drops, making the robot think there's a staircase where there isn't one, so it avoids the area.
FIX 1) Flip the robot over. 2> You'll see small, clear plastic windows near each wheel. These are the cliff sensors. Clean them thoroughly with a dry Q-tip or soft cloth. 3) Also, check the corresponding reflective surface right next to each sensor window and clean that too. 4) The problem is most common on very dark, shiny floors (black tile, dark hardwood) that don't reflect the sensor's light back properly. Try turning off the cliff sensors in the app's settings if you have no actual drop-offs, but do this with caution.
IF THAT DIDN'T WORK Strong, direct sunlight flooding the floor can also blind the sensors. Try running it at a different time of day or closing the blinds to see if the behavior changes.
HEADS UP Don't use glass cleaner or liquids directly on the sensor windows. Moisture can seep in and damage them. A dry microfiber cloth is all you need. If the problem only happens on specific rugs, the pattern or fringe might be tricking the sensors.