Answer
Run Compile Invalid Objects (Solution Manager > System Information and Utilities > Oracle Objects) right after every deployment — a deployment can leave unrelated PL/SQL packages in an invalidated state in Oracle's dependency tracking, and any session or job that tries to call into one of those invalidated packages before it's recompiled hits exactly this kind of ORA-04061/ORA-06508 error. Explicitly recompiling invalid objects as a standard post-deployment step clears this up, rather than needing to identify which specific packages got invalidated.