You could come up with a timeline that leads to this outcome with an early POD, but then you'd be 'steering' the timeline to get a desired result. In a more realistic timeline, with a rather later POD - the problem is that is if the ERE is reduced to nothing but Constantinople, the Turks will just keep trying until they get it.
I think you'd have to prevent Bulgaria from weakening as it did as of the mid-thirteenth century in OTL. No Turkish conquest of the eastern Balkans, with Bulgaria as a conterweight to the Turks. They'd both like to have Constantinople, but neither wants to go to war with the other to get it. Then keep this basic situation for an extended period, with other European powers backing up and/or replacing Bulgaria as the western power. Eventually, it just becomes a fact of life that a lot of powers would theoretically like to control 'The Eastern Rome', but taking it would mean war with all the others who would also like to have it.
Constantinople, meanwhile, milks it for all it's worth, cultivating its image as the last remnant of the Roman Empire - almost a holy city, in a way - while using it's inevible neutrality to become a free haven for trade with all powers. Both those factors help to maintain its independence. No-one (in Europe, at least) really wants to be the one to destroy the last noble remnant of the Roman Empire, and you know... a free city where all sorts of dealings are possible is really quite useful. After all, sometimes you need a place to broker a dubious agreement. And there are those tricky negotiations that you won't hold at my place, and I refuse to hold at your place, but the Emperor is always willing to host such delicate events in Constantinople...
(It could be the setting for a novel: Constantinople, a city of spies and acient traditions, of a thousand shady deals and the oldest imperial throne of Christendom.)