Does motor oil break down over time with little mileage or engine hours?

It’s not a question of the oil breaking down in 3,500 miles/1 year.
Instead it is a matter of the oil likely being diluted by water vapor (a normal byproduct of combustion), as well as the potential for oil sludging to take place.

The problem with a vehicle that logs only 3,500 miles in 1 year is that–in most cases–those miles are accumulated mostly with short-distance local driving. That type of driving does not allow the engine and the oil to become hot enough to evaporate the water vapor, and the oil becomes diluted over time.

The process of dilution of the oil, coupled with an engine running on a richer than normal mixture when it is not fully warmed-up, can create the perfect storm for the formation of sludge, internal corrosion, and resulting engine damage.

Normally, I don’t trust the automated oil life monitors on cars to tell me when to change the oil, but in this case, I would suggest that you take its notification very seriously. Even if you are skeptical of an oil change being necessary at this point, the reality that you will void the warranty on your engine by failing to change the oil on the recommended schedule should prod you into action.