According to the A2A documentation here:
"Conceptually, agents operate at different levels of complexity:
Message-only Agents: Always respond with Message objects. They typically don't manage complex state or long-running executions, and use contextId to tie messages together.
..."
The current SQL DB integration only saves tasks and their related messages.
Incase the agent is a "message-only agent" (for example a chatbot that handles a conversation with the user), the messages are not saved persistently on the DB (as they are not part of a task).