Yes, the Flyby Anomaly is still an unsolved problem. Studies have found several candidates for the cause of the anomaly.
A recent study examined Juno's behavior on its Jupiter orbits, and found the anomaly there as well:
“Our conclusion is that an anomalous acceleration is also acting upon the Juno spacecraft in the vicinity of the perijove (in this case, the asymptotic velocity is not a useful concept because the trajectory is closed). This acceleration is almost one hundred times larger than the typical anomalous accelerations responsible for the anomaly in the case of the Earth flybys. This was already expected in connection with Anderson et al.’s initial intuition that the effect increases with the angular rotational velocity of the planet (a period of 9.8 hours for Jupiter vs the 24 hours of the Earth), the radius of the planet and probably its mass.”
Some possible origins of the anomaly have been discarded:
It is important to emphasize that this anomaly is also observed in the ranging data and cannot be attributed to a conventional or unconventional issue related entirely to the Doppler tracking. A primary evaluation of the possible conventional physical effects with could be contributing to the anomaly was carried out by Lämmerzahl et al. . Ocean tides and a coupling of the spacecraft to the tesseral harmonic terms in the geopotential model have also recently been studied 2. Atmospheric friction can also be dismissed except for flybys at altitudes of 300 km or lower . The same can be said of the corrections corresponding to General Relativity [28, 26], thermal effects  or other .
But the study found no conclusive cause for the anomaly:
Summarizing, we can say that in this paper: (i) We have found evidence
that an anomaly could be operating also during the Juno flybys of Jupiter (ii) We have developed a theoretical model to compare with the orbital model
fitted to telemetry data in order to disclose the form of the possible anomalous acceleration field acting upon the spacecraft. A significant radial component was found and this decays with the distance to the center of Jupiter as expected from an unknown physical interaction. (iii) The anomaly shows an asymmetry among the incoming and outgoing branches of the trajectory and this could be suggestive of a non-conservative interaction. The confirmation of these conclusions would require further independent analysis and we hope that our work will stimulate future research in this and other planetary flybys.
Another paper studied Juno's Earth flyby, and found that inaccuracies of the geopotential model (Earth's gravity field) used to model the flyby could account for the flyby anomaly:
The only perturbation that we examined that was found to be capable of producing something detectable in real-time and comparable to the predicted flyby velocity anomaly was truncation in the Earth’s geopotential model. Previously, we had found a 10x10 degree/order field sufficient for supporting launch operations. The uncertainties in the trajectory during that phase were large enough as to not require a higher fidelity model. However, for the EGA flyby we found that the perturbation caused by including the additional effect of the higher degree and order terms was as large as 4.5 mm/s when using a 50x50 field.
Another paper concluded that solar radiation pressure is another candidate:
Solar radiation pressure presented more interesting results: small changes in the solar radiation pressure coefficient CR could explain the anomaly. In more detail, uncertainties in the values of the reflectivity coefficients of the materials that cover the spacecraft could be held responsible for the anomalous velocity change observed. Actually, we proved that modifications of the specular and diffuse reflectivity coefficients by an amount ranging from 10−4 to 4*10−2 are sufficient to successfully eliminate the unexpected velocity shift at perigee.