The rule you're looking for is [url=https://webdiplomacy.net/datc.php#section6]DATC 6.F.4[/url]
6.F.4 - TEST CASE, AN ATTACKED CONVOY IS NOT DISRUPTED

Basically, unlike supports, convoys are not disrupted if only tapped; they must be dislodged to break the convoy. In short, the adjudication was handled correctly.

What happened in your case is that Serbia to Bulgaria with support from Rumania (Greece's support was cut), and Ankara to Bulgaria (convoyed by Black) with support from Constantinople, bounced.

I certainly understand your confusion, however. The convoy line has a red X over it, implying it failed. It did not. Although I'm not at all familiar with the map-drawing code, I suspect because the convoyng army bounced, even if the convoy did occur, the map-drawing script puts X's through the convoy in addition to the movement arrow itself.

Although nothing was handled incorrectly, this doesn't seem to be a sensible way to handle tapped convoys. I'll submit a bug report to our Github.

EDIT: What Aurelin said...

Convoys are stronger than supports. If a convoying fleet is attacked but not dislodged, the convoy continues. So a convoy is only stopped if Black Sea is dislodged.

Hope that helps!

https://webdiplomacy.net/map.php?gameID=242907&turn=3&mapType=large

Serbia to Bulgaria was supported by Rumania
Ankara to Bulgaria was supported by Constantinople, convoyed by Black Sea

But I would have expected Sevastopol to Black Sea to break the convoy, and therefore Serbia to Bulgaria to succeed.

Why does a broken convoy bounce out an equally supported attack?