...Is the problem of tracking lunar satellites still an unresolved one?...
tl;dr: On July 2, 2016 the location of the at-the-time-dead Chandrayaan-1 spacecraft orbiting the Moon was determined by transmitting radar pulses from the Goldstone radar dish and receiving reflections with the Green Bank observatory.
This demonstration shows that it's possible, and that it is non-trivial to do radar detection and tracking of small spacecraft at the distance of the Moon.
There are now proposals both in China and the West to build dedicated deep-space radar networks.
- Does transmitting from a few dishes significantly improve the performance of radar surveillance from Earth at GEO and beyond? If so, how exactly?
- this answer to How can we install a radar on radio telescopes like FAST or GMRT?
- What would be a "big picture" understanding of how the orbits of Earth satellites are monitored?
- What will China's new "space station" in Argentinian Patagonia be used for?
- How did Argentina, Namibia, and Pakistan help China monitor and communicate with Chang'e 5?
Tracking is much, much easier and more accurate if the spacecraft is "not quite dead" and has at least a functioning coherent transponder.
If the spacecraft is dead
Tracking is something usually done from Earth. If the spacecraft is dead or has only passive radar reflectors, then radar or lidar active tracking will be needed.
- How does the SpaceBEEs' experimental passive radar reflector work?
- Are SpaceBEEs actually hard to track?
- Why was the 100m Green Bank dish needed together with DSN's 70m Goldstone dish to detect Chandrayaan-1 in lunar orbit?
If the spacecraft's coherent transponder is still working
If the spacecraft is still at least partially alive and it's coherent transponder is still operational, then it can receive signals from a tracking station (radio or optical) and turn them around and send them back to the same, or a different tracking station.
Then Earth can measure the total light time of the signal and its doppler shift to measure distance and radial velocity. If you make several measurements like this for something orbiting the Moon you can rapidly converge on its position and orbit with great accuracy. (The position of the Moon itself relative to Earth is known down to centimeters!)
When separate transmit and receive stations, or better yet two simultaneous receive stations are used, you can also use VLBI (very long baseline interferometry) along with the range-rate data to pinpoint the location.
- this answer to Have various lunar rovers known their own position on the Moon? If so, how?
- this answer to What are monostatic radar observations, and how will Deep Space Network's DSS-13 be used to observe asteroid 1999 WK4's flyby of Earth?
- Tradeoffs between using two 34 m and one 70 m Deep Space Network dish?
- How does a third DSN station serves as a “relay” to tie-together observations by two other stations doing VLBI?
- How are precision trajectory measurements made of trans-Neptunian spacecraft?
VLBI tracking in cis-lunar space was tested and refined using lunar rovers and the ALSEP telemetry radio transmitters left on Moon by Apollo lander missions.
- Were the Apollo lunar ALSEP transmitter signals ever analyzed or used after the experiments were shut down?
- Were there any policies or technical reasons for powering down all Apollo ALSEPs in 1977?
- Why were the "perfectly functioning" seismometers placed by Apollo 12, 14, 15 and 16 astronauts all shut off in 1977?
VLBI will be used to measure the location of the JWST in its halo orbit 1.5 million kilometers from Earth down to centimeters of accuracy. This is absolutely necessary to drive its delta-v budget for station keeping in its orbit to just a few meters per second per year. Part of the trick is also to use the solar shield as a solar sail (the Sun's photon pressure helps hold it in place just to one side of it's most stable halo orbit distance), but there's not much flexibility since it can't be steered completely independently from the telescope. (There is one axis of rotation possible; for some observations the telescope doesn't care how it is rotated around its optical axis).
But what about GPS?
- What is the deepest position in space we can get a GPS signal?
- How far up have satellites used a GNSS for positioning, and how does the precision degrade with altitude?
- How to estimate that receiving GNSS signals Earth while orbiting the Moon will still provide locations to about 200 meters of uncertainty?
...or near-future technologies?
Beacons or even coherent transponders could also work using light pulses rather than radio waves. In 10 to 100 Gbit/sec optical telecommunications the light pulses are only of order a centimeter long. The light beam itself does not necessarily have to be coherent, only the pulse train.
- Long delay-doppler measurements on deep space craft; couldn't optical measurements be made intermittently, mixed with contacts to other spacecraft?
- Quantitatively, why will optical communication be better than X-band for deep-space communications?
- How did LADEE and LDRC measure it's distance from Lunar orbit to Earth to 1 centimeter accuracy using optical communications?
- How is long-distance optical communications coming along in space?
- What's the current timeline for NASA's Mars orbiter laser communications?
...or not-so-near-future technologies?
Beacons or even coherent transponders could also work using X-ray pulses rather than light pulses or radio waves.
Those pulses could be from artificial X-ray beacons, or they could be pulsars!
- Is NICER/SEXTANT the first civilian "spacecraft" to determine it's own position in space without GPS or uplinked data?
- How will NavCube (actually) be important for the XCOM testing and demonstration?
- What will the X-ray communications (XCOM) transmitter look like?
The role of deep space atomic clocks
For single beacons to be particularly helpful the spacecraft needs to know what time it is to nanosecond accuracy. Luckily there's a solution for that coming up.
- How is Lucy "making use" of a deep space atomic clock?
- Where would one deploy deep space atomic clocks?
- How does an onboard atomic clock help interplanetary navigation?
- Help understanding exactly how an atomic clock facilitates “self-driving spacecraft” when paired with an onboard camera?
- Why does the Deep Space Atomic Clock have such a short mission?
- How high is the first Deep Space Atomic Clock orbiting? Does it receive radiation equivalent to that in deep space?
- How far from earth have atomic clocks (or ultra-stable oscillators) been placed and monitored?
related questions (the OP already has some familiarity with the topic!)
- Could a satellite use a Miniature Atomic Clock (MAC) to provide GPS services?
- Have various lunar rovers known their own position on the Moon? If so, how?
- Could a single CubeSat provide location services on another celestial body such as Mars? Could a constellation do it?
above: "This computer-generated image depicts the Chandrayaan-1's location at time it was detected by the Goldstone Solar System radar on July 2, 2016. The 120-mile (200-kilometer) wide purple circle represents the width of the Goldstone radar beam at lunar distance. The white box in the upper-right corner of the animation depicts the strength of echo. Inside the radar beam (purple circle), the echo from the spacecraft alternated between being very strong and very weak, as the radar beam scattered from the flat metal surfaces." Credit: NASA/JPL-Caltech. From here