For several months it looked like Kosmos-2568 would follow the same mission profile as the three earlier EO MKA satellites (Kosmos-2551, 2555, 2560), slowly decaying without performing any orbit corrections. However, that pattern abruptly changed on August 9, by which time its orbit had decayed to roughly 287x300 km. Since then the satellite has clearly been performing minor burns to counter further decay (see the graph from Celestrak). It is currently being tracked in a 287x298 km orbit. The orbit corrections have been very minor. The most significant one thus far took place on August 14, when it lowered its perigee and raised its apogee by roughly one kilometer. There may also have been some small tweaks in late June/mid-July, but the data for those is less convincing.
So Kosmos-2568 clearly has some kind of thruster system. The question is why it was not activated until more than four months into its mission and why its three predecessors did
not maneuver.
I was able to make several visual observations of Kosmos-2568 in June and early July. On most passes it was a relatively bright naked-eye object, reaching magnitude +2.5-3.0 (somewhat fainter than Polaris, the North Star). I had two more opportunities to see it in early August, but by that time the observing conditions were much less favorable (it came out of the Earth’s shadow much later) and I could no longer see it with the naked eye. There are no more visible passes from the northern hemisphere now.
At its brightest, it was about the same magnitude as a Soyuz or Progress, but since it was launched by a Soyuz-2-1v, it must be significantly smaller. This would indicate it has a quite reflective surface (Soyuz/Progress, on the other hand, have dark thermal insulation). If it is really an “MKA” (a Russian acronym for “small satellite”), then by the Russian definition of that term it should be no heavier than about 1 ton. In theory it could be twice as heavy though. According to data from RKTs Progress, the Soyuz-2-1v (without the Volga upper stage) has a payload capacity of 2.43 tons to a 200 km, 98.7° orbit from Plesetsk.