It is not that it is blocked by the Sun, but that the duration of time for which it can be continuously observed was too small to be useful for the investigations performed in the paper.
The object was observed by XMM-Newton, which has a highly eccentric ($e \sim 0.8$), 48-hour orbit arond the Earth. This is designed so that the satellite can stare for relatively long periods at the same object, whilst being beyond a lot of the geocoronal background that interferes with its detectors. Whilst doing so it has to avoid looking (i) close to the Sun; (ii) close to the Earth; (iii) at the Moon.
The "visibility" of a target is defined as the longest continuous time it can be observed before the satellite has to break-off and point somewhere else. This can be as long as 140,000 s (there's a deadspot where they switch the detectors off when near the Earth), but can often be much shorter (or zero) at any paticular time. For efficiency reasons, the satellite operations team don't want to schedule too many short-visibility observations, since this wastes valuable observing time and spacecraft resources, and scientifically you often don't want to use short-visibility windows because you want to observe some sort of variability over a certain duration (e.g. observing over a full eclipsing binary orbit, or looking for variablity on a variety of timescales and requiring a long continuous time-series to get enough signal-to-noise in the Fourier spectrum).
Since the position of the Earth, Moon and Sun change with respect to each other, the visibility of an object will change from orbit-to-orbit of the satellite. Furthermore, because the orbit of XMM-Newton changes with time in quite a complex way (it precesses and the eccentricity has changed a little bit over the years), then the exact visibility of an object will not repeat from year-to-year and some objects will "come into season" during different years. In some cases sources can go through epochs where they are not continuously visible for long periods of time. For this particular position in the sky there appears to have been an unfortunate gap of about 7 years (that is actually the gap between observations, but I haven't checked whether that was completely determined by lack of "visibility" or what the maximum "visibility" was during those 7 years) when the object was not continuously observable for the $\sim 70,000$ seconds required by the science.
I managed to find this old plot, produced not long after XMM-Newton was launched. It shows the maximum visibility versus position on the sky for orbits 3-432 (about the first 2.5 years of operation). This shows that there is a fairly substantial patch of sky which was not continuously observable for more than about 50,000 s for the whole of that period.
There is a more modern interactive map here. This was for "AO-19" (May 2020 - May 2021), and is used by astronomers proposing observations to check how long an object is continuously visible for (as a fraction of the maximum possible time of around 140,000 s; actually there is a detailed web calculator to do it for any position). You can see that in this 12 month period there are big areas that cannot be observed for very long.
NB: There's nothing special about the object coordinates. Ecliptic coords 144, +28, though I would think that high ecliptic latitudes are less likely to be afflicted by this problem, since you would always be pointing at a large angle from the Sun.