Why don’t current-day Yugoslavians speak a Latin-based language but Romanians do?

They did:

• Dalmatian language – Wikipedia
• Istro-Romanian language – Wikipedia
• Aromanian language – Wikipedia
• Megleno-Romanian language – Wikipedia

What happened is quite simple: Slavic tribes moved into the area quite rapidly, between 500 and 800. Slavonic displaced Romance languages in most areas they moved into, with a few enclaves surviving.

The real question is not why don’t Yugoslavians speak Romance, but why Romanians do over such a wide area. Origin of the Romanians – Wikipedia shows that there is not a consensus around it, and of course the question is clouded by politics.

• Either there was a continguous compact Latin-speaking population in Romania, which resisted Slavonic assimilation (Theory of Daco-Roman continuity);
• or Romania was resettled by Latin-speaking populations (Aromanians) from enclaves south of the Danube (Immigrationist or Admigrationist theory). The Aromanians are highland shepherds, so they were not in regular contact with Slavs settling the lowlands.