Once you are in orbit you don't need that much fuel to maintain the orbit. Over long periods of time gravitational irregularities and atmospheric drag do cause low earth orbit satellites to fall out of orbit and burn up but these effects are minimal and only build up over time, so long as you keep things high enough and prevent them from dipping back into the atmosphere they can maintain an orbit for many years on a small amount of fuel.

The voyager probes were able to go past all those planets without falling into an orbit essentially because they were going way to fast. The point of the voyager probes was essentially to fly them out as quickly as possible during a planetary conjunction that allowed for relatively easy access so they could snap pictures. The consequence of sending them out quickly is that they are going too fast to stop afterwards so they just fly past. It was the same with the recent probe to Pluto, in order to get the probe there in a reasonable amount of time, which is still more than a decade, they need to fly it so fast that it's prohibitively expensive to slow it down and insert it into an orbit on the other end.