The only scenario I can see where it would bed pulled is if the BBC's own rules mandated that all iplayer apps must have BBC ID login. It seems likely that the current ATV iplayer app was the result a one of payment from Apple to the BBC (and by the low quality of the final product, it was a small payment), so unless Apple pay up again, it could be removed as the BBC wouldn't pay for the work.
That said even with Apple's get low level of interested in any country not called America I can't see them letting the BBC remove it. It's a bad app, but it's also one of the essentials, along with Netflix and Amazon.
Apple didn't pay the BBC to develop an iPlayer app. The BBC can only accept money from the licence fee and BBC Worldwide.
I remember a few years back Russell T Davies (filming his last episode of Doctor Who) revealed that he wanted to help pay for a scene deemed too expensive for a BBC show but was refused as the BBC cannot accept money from outside sources, even from the showrunner himself!
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With great "pay for our programming or you'll go to jail" programming like East Enders, DIY SOS and Strictly Come Dancing I don't know why HBO even bother to compete.
Ahh the joys of cherry picking.