Stars' proper motion

When setting the date to the far future (or past), stars shift positions and constellations appear different as expected. However, certain stars (doubles?) move in unreasonable ways. For instance, center image on Rigil Kentaurus. Then shift date to year 12000. The star has moved relative background but alfa Centauri B now appears over a degree away from A. This distance seems to increase with how far into the future one is looking.
When looking farther into the future (year 32000), Rigil Kentaurus is only visible when zooming out and cannot be highlighted (but alfa Centauri B, far away from it, can). When zoming in on the highlighted star, it disappears.