Not so much a bug as a design mistake; but I'll certainly take the blame for it. I'm fixing this for the next engine update.
In the interest of fast gameplay, Arena really doesn't want you to have priority during many steps and phases, including your own End Step. We added a special provision in the last update for your opponents flashing in permanents, but included logic to clear out the flag that could give you further priority whenever you took an action.
We expected players who wanted to perform multiple actions here would put a manual stop in the step or go into full control. Clearly that's not the case; we've gotten quite a few complaints here! So next time, we're only clearing the flag when players move on from the step/phase where the special stop was triggered. #wotc_staff