The rejection goes away when you do anything else

An overlay that lasted until the next accepted evaluation was a durable
annotation on the source, which is not what it is: it is feedback about the
action that just failed, and the moment you move, type or evaluate it is
describing a program state nobody is in any more.

pre-command-hook rather than post-command-hook, which fires at the end of
the failing command and would take the overlay down before redisplay ever
drew it. Buffer-local and installed only while an overlay exists, so a
session of twenty buffers does not end up running this on every keystroke
in all of them.

emacs/flan-dev.el

@@ -731,9 +731,27 @@ Compared with `file-equal-p', so a symlinked or relative path still matches."
 
 ;; An error is shown where it is rather than only in the echo area, because the
 ;; echo area is gone the moment you type and the location is the useful half of
-;; the message.  It is cleared when the next evaluation of that buffer is
-;; accepted: an overlay left behind after a fix is a lie about the program, and
-;; a stale one is worse than none.
+;; the message.
+;;
+;; It is feedback about the evaluation that just failed and not an annotation
+;; on the source, so it lasts exactly as long as that: the next command in that
+;; buffer takes it away, whatever the command was — a keystroke, a motion,
+;; another evaluation.  An overlay that survived until some later evaluation
+;; was accepted outlived the thing it was about, and a stale one is worse than
+;; none.
+;;
+;; `pre-command-hook' and not `post-command-hook': the hook has to run before
+;; the *next* command, because `post-command-hook' fires at the end of the
+;; failing command itself and would take the overlay down before redisplay had
+;; ever drawn it.
+;;
+;; The hook is buffer-local and lives exactly as long as an overlay does —
+;; added where one is drawn, removed where they are cleared.  Globally it would
+;; be a hook every buffer in the session runs on every keystroke for the sake
+;; of a feature most of them will never use; buffer-locally it is also the
+;; behaviour asked for, since the overlay belongs to the buffer the failed
+;; evaluation came from and a command somewhere else is not "doing something
+;; else in that buffer".
 
 (defface flan-dev-error-face
   '((t :inherit error :underline (:style wave)))
@@ -749,7 +767,19 @@ Compared with `file-equal-p', so a symlinked or relative path still matches."
   "Remove Flan error overlays from BUFFER, or from the current buffer."
   (interactive)
   (with-current-buffer (or buffer (current-buffer))
-    (remove-overlays (point-min) (point-max) 'flan-dev-error t)))
+    (remove-overlays (point-min) (point-max) 'flan-dev-error t)
+    ;; With nothing left to clear there is nothing for the hook to do, and a
+    ;; hook that stays installed after the last overlay is gone is the half of
+    ;; this that quietly accumulates.
+    (remove-hook 'pre-command-hook #'flan-dev--clear-errors-on-command t)))
+
+(defun flan-dev--clear-errors-on-command ()
+  "Take this buffer's error overlays down, as a `pre-command-hook'.
+Any command at all, because the overlay is about the evaluation that failed
+and not about the text: moving, typing and evaluating are all something
+else, and an overlay that survived a fix would be pointing at code that is
+no longer wrong."
+  (flan-dev-clear-errors))
 
 (defun flan-dev--show-error (loc msg)
   "Mark MSG at LOC, if LOC names a file some buffer is visiting.
@@ -771,6 +801,10 @@ Returns non-nil when it put an overlay somewhere."
               (overlay-put ov 'after-string
                            (propertize (concat "  " msg)
                                        'face 'flan-dev-error-message-face))
+              ;; Local to this buffer, and installed only now that there is
+              ;; something for it to remove.
+              (add-hook 'pre-command-hook
+                        #'flan-dev--clear-errors-on-command nil t)
               ;; Point goes there too, but only in the buffer being looked at:
               ;; moving point in a buffer nobody is showing is a surprise the
               ;; next time it is visited.
@@ -1079,6 +1113,10 @@ of the tenth name tells you neither how many there were nor which."
             (note (plist-get reply :note))
             (value (plist-get reply :value)))
         ;; Accepted, so whatever the last rejection marked is no longer true.
+        ;; Redundant now that any command clears it — the command that ran this
+        ;; evaluation already did — and kept because it is the claim being
+        ;; made, not the mechanism: an accepted evaluation is never left with a
+        ;; rejection drawn over it.
         (flan-dev-clear-errors)
         ;; ...and a name that was just installed should complete, and have a
         ;; signature, from this moment rather than from the next connect.