Experience orbs from killing mobs, mining, and fishing are sometimes not absorbed by the player. They will follow the player and spin around them, but they will not absorb. This seems to happen quite frequently.
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What does that mean, unload the chunk?

The plauer has a default 4 chunk ticking area in which the game processes events in the game. When you leave an area and go about 90 blocks or more the game will unload the areas outside that ticking area and save into memory all entities in the unloaded 'chunk'. So that could cause the xp orbs to be unloaded and sometimes cannot be absorbed by the player.
More about chunks and ticking area in the wiki.

So they're unloading while I'm standing there trying to pick up the orb?

Oh....did you not leave the area before you picked up the xp or did you reopen the game when there were xp near you? Because that's what happens to me when I leave the area.

No. I kill the thing. And experience orbs twirl around me and don't absorb.

Strange...seems to happen more common on console. I played on W10 and PE but this will only happen if I leave the xp orbs in an unloaded chunk for too long.
Thank you for your report!
However, this issue has been closed as a Duplicate of MCPE-11181.
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Seems to happen whenever the player unloads the chunk without collecting the xp.