📝 clarify async status helper docs

docs/api/async-logger-has-failed.md

@@ -36,6 +36,7 @@ Detailed rules explaining key parameters and behaviors
 - `run()` clears previous failure state at startup.
 - `run()` also clears the stored `last_error()` string at startup before drain work begins.
 - If the worker loop raises an error, the logger records that failure and exposes it through this flag.
+- Once set by a failed run, the flag stays `true` until a later `run()` start resets it.
 - This helper is intentionally compact and should usually be paired with `last_error()` for details.
 - Failure state is about runtime drain execution, not whether records were dropped due to overflow policy.
 
@@ -72,6 +73,8 @@ e.g.:
 
 - If `has_failed()` is `true`, callers should inspect `last_error()` or `state()` for more context.
 
+- `close()` or `shutdown()` do not clear this flag by themselves; only a later `run()` start resets it.
+
 ### Notes
 
 1. This helper reports worker failure, not general queue stress.