Index: src/js/_enqueues/lib/image-edit.js
===================================================================
--- src/js/_enqueues/lib/image-edit.js	(revision 56591)
+++ src/js/_enqueues/lib/image-edit.js	(working copy)
@@ -245,6 +245,37 @@
 	},
 
 	/**
+	 * Observes whether the popup should remain open based on focus position.
+	 *
+	 * @since 6.4.0
+	 *
+	 * @memberof imageEdit
+	 *
+	 * @param {HTMLElement} el The activated control element.
+	 *
+	 * @return {boolean} Always returns false.
+	 */
+	monitorPopup : function(el) {
+		var $el     = $( el );
+		var $parent = document.querySelector( '.imgedit-rotate-menu-container' );
+		var $toggle = document.querySelector( '.imgedit-rotate-menu-container .imgedit-rotate' );
+
+		setTimeout( function() {
+			var $focused = document.activeElement;
+			var $contains = $parent.contains( $focused );
+
+			// If $focused is defined and not inside the menu container, close the popup.
+			if ( $focused && ! $contains ) {
+				if ( 'true' === $toggle.getAttribute( 'aria-expanded' ) ) {
+					imageEdit.togglePopup( $toggle );
+				}
+			}
+		}, 100 );
+
+		return false;
+	},
+
+	/**
 	 * Navigate popup menu by arrow keys.
 	 *
 	 * @since 6.3.0
Index: src/wp-admin/includes/image-edit.php
===================================================================
--- src/wp-admin/includes/image-edit.php	(revision 56589)
+++ src/wp-admin/includes/image-edit.php	(working copy)
@@ -63,7 +63,7 @@
 			<button type="button" onclick="imageEdit.toggleCropTool( <?php echo "$post_id, '$nonce'"; ?>, this );" aria-expanded="false" aria-controls="imgedit-crop" class="imgedit-crop button disabled" disabled><?php esc_html_e( 'Crop' ); ?></button>
 			<button type="button" class="imgedit-scale button" onclick="imageEdit.toggleControls(this);" aria-expanded="false" aria-controls="imgedit-scale"><?php esc_html_e( 'Scale' ); ?></button>
 			<div class="imgedit-rotate-menu-container">
-				<button type="button" aria-controls="imgedit-rotate-menu" class="imgedit-rotate button" aria-expanded="false" onclick="imageEdit.togglePopup(this)"><?php esc_html_e( 'Image Rotation' ); ?></button>
+				<button type="button" aria-controls="imgedit-rotate-menu" class="imgedit-rotate button" aria-expanded="false" onclick="imageEdit.togglePopup(this)" onblur="imageEdit.monitorPopup(this)"><?php esc_html_e( 'Image Rotation' ); ?></button>
 				<div id="imgedit-rotate-menu" class="imgedit-popup-menu">
 			<?php
 			// On some setups GD library does not provide imagerotate() - Ticket #11536.
@@ -75,9 +75,9 @@
 			) ) {
 				$note_no_rotate = '';
 				?>
-					<button type="button" class="imgedit-rleft button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.rotate( 90, <?php echo "$post_id, '$nonce'"; ?>, this)"><?php esc_html_e( 'Rotate 90┬░ left' ); ?></button>
-					<button type="button" class="imgedit-rright button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.rotate(-90, <?php echo "$post_id, '$nonce'"; ?>, this)"><?php esc_html_e( 'Rotate 90┬░ right' ); ?></button>
-					<button type="button" class="imgedit-rfull button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.rotate(180, <?php echo "$post_id, '$nonce'"; ?>, this)"><?php esc_html_e( 'Rotate 180┬░' ); ?></button>
+					<button type="button" class="imgedit-rleft button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.rotate( 90, <?php echo "$post_id, '$nonce'"; ?>, this)" onblur="imageEdit.monitorPopup(this)"><?php esc_html_e( 'Rotate 90┬░ left' ); ?></button>
+					<button type="button" class="imgedit-rright button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.rotate(-90, <?php echo "$post_id, '$nonce'"; ?>, this)" onblur="imageEdit.monitorPopup(this)"><?php esc_html_e( 'Rotate 90┬░ right' ); ?></button>
+					<button type="button" class="imgedit-rfull button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.rotate(180, <?php echo "$post_id, '$nonce'"; ?>, this)" onblur="imageEdit.monitorPopup(this)"><?php esc_html_e( 'Rotate 180┬░' ); ?></button>
 				<?php
 			} else {
 				$note_no_rotate = '<p class="note-no-rotate"><em>' . __( 'Image rotation is not supported by your web host.' ) . '</em></p>';
@@ -88,8 +88,8 @@
 			}
 			?>
 					<hr />
-					<button type="button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.flip(1, <?php echo "$post_id, '$nonce'"; ?>, this)" class="imgedit-flipv button"><?php esc_html_e( 'Flip vertical' ); ?></button>
-					<button type="button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.flip(2, <?php echo "$post_id, '$nonce'"; ?>, this)" class="imgedit-fliph button"><?php esc_html_e( 'Flip horizontal' ); ?></button>
+					<button type="button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.flip(1, <?php echo "$post_id, '$nonce'"; ?>, this)" onblur="imageEdit.monitorPopup(this)" class="imgedit-flipv button"><?php esc_html_e( 'Flip vertical' ); ?></button>
+					<button type="button" onkeyup="imageEdit.browsePopup(this)" onclick="imageEdit.flip(2, <?php echo "$post_id, '$nonce'"; ?>, this)" onblur="imageEdit.monitorPopup(this)" class="imgedit-fliph button"><?php esc_html_e( 'Flip horizontal' ); ?></button>
 					<?php echo $note_no_rotate; ?>
 				</div>
 			</div>