No Crusader Sack of Constantinople in 1204

It would depend on what the reason was. I.e. does the empire avoid the infighting that gave an excuse for the crusaders intervention and made their victory possible. Or simply the attempted attack is defeated, possibly with heavy crusader losses. Or even for some reason the Papacy's opposition to the operation becomes known and persuades the crusaders not to attack the city.

If the empire is better lead, defeats the attack and has a period of relative stability it might be able to stage a recovery, albeit more difficult than in earlier centuries. Without the western intervention and establishment of the assorted Catholic ruled states while there might be more tension between Orthodox and Catholic churches the empire is at the very least going to be able to resist the Ottomans and other Turks longed and might even be able to drive them back substantially.

Mind you by this stage the Mongols are aready on the march so at some point in the following decades large steppe armies are likely to threaten both the Danube and Anatolian frontiers. This could be a disaster for the empire if it is strong enough and rich enough to decide to oppose the Mongols and prompt an all out attack. Or they could end up allying with the Mongols against the Muslims and ending up winning massively. [At least unless and until someone like Tamerlain comes along].