Presumably this is because solar power isn't feasible at large
distances from the Sun.
There is a possibility to use solar energy as long as the arrays receive a quantity of energy greater than the working level of a photo voltaic cell. This includes the full solar system. The solar cell usability under low intensity is constantly improving.
But, right... being able to collect only very little energy is not sufficient to power any space probe for the time being.
With the current technology available, what is considered the "safe
zone" that solar arrays can be used as a reliable source to power a
The energy required for a given mission can be obtained by adjusting the size of the solar arrays, but this adjustment has an upper limit. The other way it to use more efficient cells:
"Cell efficiencies are measured under standard test conditions (STC) unless stated otherwise. STC specifies a temperature of 25 °C and an irradiance of 1000 W/m² with an air mass 1.5 (AM1.5) spectrum. [...] This represents solar noon near the spring and autumn equinoxes in the continental United States with surface of the cell aimed directly at the sun."
Cells work outside of STC very well, as soon as working conditions are taken into account in the design:
"Inner planetary missions and missions to study the sun within a few solar radii require solar arrays capable of withstanding temperatures above 450 °C and functioning at high solar intensities (HIHT). Outer planetary missions require solar arrays that can function at low solar intensities and low temperatures (LILT). In addition to the near-sun missions, missions to Jupiter and its moons also require solar arrays that can withstand high-radiation levels."
(Source: Space Solar Cells and Arrays - Bailey, Raffaelle)
There are also different possibilities to concentrate light on cells to prevent low intensity efficiency degradation, and to obtain more energy from the same cell area:
Practical usuability of solar arrays in space
Overall, this Nasa's study (2007) assume solar arrays are practically usable as far as the Jupiter orbit (5.2 AU, Ultraflex products), and that Saturn (10 AU) mission will be achievable in near-term.
(Juno mission for Jupiter)
"Near term Ultraflex arrays and state-of-art multi junction cells can provide capability to perform low power (200-300 W) missions out to 10 AU."
However several factors are to be taken into consideration.
Size of the solar arrays
The quantity of energy received at some distance from the Sun is driven by an inverse square law. See this question on Physics.SE for more details:
"PV works great near the Earth, at 1 AU from the Sun, where we receive about 1400 Watts per square meter [...] At Saturn, nearly 10AU from the Sun, there's 1/100th power. Fine, if a spacecraft carries solar arrays 100 times bigger than would be used near Earth." -- For Juno mission: "Its 45 m² planar array produces 9.6 kW BOL at 1 AU and 414 W at 5.5 AU"
BOL / begin of life: Cells efficiency decreases with time, as they are exposed to radiations (protons, UV, IR, etc).
The first problem arises in term of arrays size to deliver the electrical energy you need, and whether the spacecraft can accommodate such size or not.
The spacecraft in orbit around a celestial body will not receive Sun light when behind this body. Some energy storage mean is required.
A celestial body may reflect Sun light to the probe arrays, increasing energy production.
Robustness of the arrays
Arrays may be destroyed during launch, or in orbit by debris. As they become larger their robustness is difficult to maintain without adding mass to the system.
Cost of the launch
The larger the energy required, or the further the spacecraft from the Sun, the more expensive the arrays due to their size. The cost of the launch is also impacted due to the corresponding variation in mass.
At some point other sources of energy will become cheaper to build and to launch.
Maximum current output
If the mission has a need for more current than the arrays are able to produce, and it's not suitable to increase the arrays size then energy must be stored at the rate the array can deliver it, then consumed at the higher rate required until the battery is empty, and then wait for the battery to be charged again.
Working discontinuously may be acceptable or not. In addition battery effectiveness decreases over time, and dust or propellant may dim the solar radiations. Long missions may not be able to accommodate these issues.