A supplementary answer, in response to @JessRiedel's comment:
this answer does not apply to communication from the satellite to Earth, for which it is reasonable to consider communication relay sats.
(quoting because comments can vanish).
There are two problems, broadly speaking: orbital dynamics and economics.
Orbital dynamics means that you can't keep a satellite permanently half way from Earth to Jupiter. After a few years, the various orbital motion under the effect of the Sun's gravity will have moved things so it's actually further from Jupiter than Earth is. So any such relay is either a one-shot for a particular mission for a relatively short period, or you need a whole lot of them spaced out around an orbit, which is getting crazy expensive.
The economic problem is essentially a variant of the uplink considerations in @djr's answer: it's almost always cheaper to upgrade facilities on Earth than to put something in space big enough to be useful. Let' try some numbers: Suppose we put a relay half way between the probe and Earth. On Earth we have a very high quality 70m dish and absolutely state of the art amplifiers, unlimited power to run those amplifiers, liquid helium to cool them, etc. If our relay is half way between Earth and the target, and somehow manages to have a 70m antenna of its own (massively bigger than anything ever flown) of the same quality and equally good amplifiers and signal processing it will quadruple the available data bandwidth. We could alternatively do that by building three more 70m antennae on Earth and linking them (a well-developed technology). Not only would that be massively cheaper, but they could be used for other purposes when not needed.
What is useful and has been done, is for a bunch of small probes in the same part of the solar system at the same time to relay their communications through one "mother ship". It means you only have to budget the mass for a 2 or 3 metre antenna and a relatively powerful transmitter, once, and you can put the relay in an orbit where it will usually be visible from Earth. This is happening now for Mars missions. If there were a flurry of missions to the Jupiter system, for example, the same approach would be worthwhile -- put a comms relay in high Jupiter orbit and have all the missions relay through it using less massive and power hungry systems.