diff --git a/client/src/controllers/DropdownController.ts b/client/src/controllers/DropdownController.ts
index e1533bfb9869..b80229dda1ce 100644
--- a/client/src/controllers/DropdownController.ts
+++ b/client/src/controllers/DropdownController.ts
@@ -95,20 +95,22 @@ export class DropdownController extends Controller<HTMLElement> {
   static targets = ['toggle', 'content'];
   static values = {
     hideOnClick: { default: false, type: Boolean },
+    keepMounted: { default: false, type: Boolean },
     offset: Array,
     theme: { default: 'dropdown' as TippyTheme, type: String },
   };
 
   // Hide on click *inside* the dropdown. Differs from tippy's hideOnClick
   // option for outside clicks that defaults to true and we don't yet expose it.
-  declare hideOnClickValue: boolean;
-  declare offsetValue: [number, number];
+  declare readonly hideOnClickValue: boolean;
+  declare readonly keepMountedValue: boolean;
+  declare readonly offsetValue: [number, number];
+  declare readonly hasOffsetValue: boolean;
+  declare readonly themeValue: TippyTheme;
 
   declare readonly contentTarget: HTMLDivElement;
   declare readonly hasContentTarget: boolean;
-  declare readonly hasOffsetValue: boolean;
   declare readonly toggleTarget: HTMLButtonElement;
-  declare readonly themeValue: TippyTheme;
 
   tippy?: Instance<Props>;
 
@@ -144,10 +146,22 @@ export class DropdownController extends Controller<HTMLElement> {
       });
     }
 
-    const onShow = () => {
+    const onCreate = (instance: Instance<Props>) => {
+      if (this.keepMountedValue) {
+        const { popper } = instance;
+        this.element.append(popper);
+        popper.hidden = true;
+      }
+    };
+
+    const onShow = (instance: Instance<Props>) => {
       if (hoverTooltipInstance) {
         hoverTooltipInstance.disable();
       }
+      if (this.keepMountedValue) {
+        const { popper } = instance;
+        popper.hidden = false;
+      }
     };
 
     const onShown = () => {
@@ -161,6 +175,14 @@ export class DropdownController extends Controller<HTMLElement> {
       }
     };
 
+    const onHidden = (instance: Instance<Props>) => {
+      if (this.keepMountedValue) {
+        const { popper } = instance;
+        this.element.append(popper);
+        popper.hidden = true;
+      }
+    };
+
     return {
       ...(this.hasContentTarget
         ? { content: this.contentTarget as Content }
@@ -171,9 +193,11 @@ export class DropdownController extends Controller<HTMLElement> {
       ...(this.hasOffsetValue && { offset: this.offsetValue }),
       getReferenceClientRect: () => this.reference.getBoundingClientRect(),
       theme: this.themeValue,
+      onCreate,
       onShow,
       onShown,
       onHide,
+      onHidden,
     };
   }
 
diff --git a/wagtail/admin/templates/wagtailadmin/shared/dropdown/dropdown.html b/wagtail/admin/templates/wagtailadmin/shared/dropdown/dropdown.html
index 15e77cd16379..d68bc38f2525 100644
--- a/wagtail/admin/templates/wagtailadmin/shared/dropdown/dropdown.html
+++ b/wagtail/admin/templates/wagtailadmin/shared/dropdown/dropdown.html
@@ -14,12 +14,21 @@
     - `toggle_classname` (string?) - additional toggle classes
     - `toggle_tooltip_offset` (string?) - Tooltip offset prop
     - `hide_on_click` (boolean?) - Whether or not the tooltip should hide when clicking inside
+    - `keep_mounted` (boolean?) - Whether or not the tooltip should keep its DOM node mounted when hidden
     - `children` - Dropdown contents (`a` and `button` elements only)
 {% endcomment %}
 
 {% fragment as class %}{% classnames 'w-dropdown' classname %}{% if theme %} w-dropdown--{{ theme }}{% endif %}{% endfragment %}
 
-<div data-controller="w-dropdown" {% if theme %}data-w-dropdown-theme-value="{{ theme }}"{% endif %} class="{{ class }}" {{ attrs }} {% if hide_on_click %}data-w-dropdown-hide-on-click-value="true"{% endif %}{% if toggle_tooltip_offset %} data-w-dropdown-offset-value="{{ toggle_tooltip_offset }}"{% endif %}>
+<div
+    data-controller="w-dropdown"
+    class="{{ class }}"
+    {{ attrs }}
+    {% if theme %}data-w-dropdown-theme-value="{{ theme }}"{% endif %}
+    {% if toggle_tooltip_offset %}data-w-dropdown-offset-value="{{ toggle_tooltip_offset }}"{% endif %}
+    {% if hide_on_click %}data-w-dropdown-hide-on-click-value="true"{% endif %}
+    {% if keep_mounted %}data-w-dropdown-keep-mounted-value="true"{% endif %}
+>
     <button type="button" class="{% classnames 'w-dropdown__toggle' toggle_label|yesno:',w-dropdown__toggle--icon' toggle_classname %}" data-w-dropdown-target="toggle"{% if toggle_aria_label %} aria-label="{{ toggle_aria_label }}"{% endif %}{% if toggle_describedby %} aria-describedby="{{ toggle_describedby }}"{% endif %}{% if toggle_tippy_offset %} data-tippy-offset="{{ toggle_tippy_offset }}"{% endif %}>
         {{ toggle_label }}
         {% if toggle_icon %}
diff --git a/wagtail/admin/templates/wagtailadmin/shared/headers/_filters.html b/wagtail/admin/templates/wagtailadmin/shared/headers/_filters.html
index 80f39b48b168..e7b4a6aa2348 100644
--- a/wagtail/admin/templates/wagtailadmin/shared/headers/_filters.html
+++ b/wagtail/admin/templates/wagtailadmin/shared/headers/_filters.html
@@ -4,7 +4,7 @@
     <span class="w-drilldown__count" data-w-drilldown-target="count" hidden></span>
 {% endfragment %}
 
-{% dropdown theme="drilldown" toggle_icon="sliders" toggle_classname="w-filter-button" toggle_aria_label=_("Show filters") toggle_suffix=toggle_suffix %}
+{% dropdown theme="drilldown" toggle_icon="sliders" toggle_classname="w-filter-button" toggle_aria_label=_("Show filters") toggle_suffix=toggle_suffix keep_mounted=True %}
     <div class="w-drilldown__contents">
         <div class="w-drilldown__menu" data-w-drilldown-target="menu">
             <h2 class="w-help-text w-pl-5 w-py-2.5 w-my-0">{% trans "Filter by" %}</h2>