diff --git a/src/plugins/es_ui_shared/public/request/request.test.js b/src/plugins/es_ui_shared/public/request/request.test.js
index 03bed758b1209..60b05a8dc8a27 100644
--- a/src/plugins/es_ui_shared/public/request/request.test.js
+++ b/src/plugins/es_ui_shared/public/request/request.test.js
@@ -98,20 +98,19 @@ describe('request lib', () => {
       describe('path, method, body', () => {
         it('is used to send the request', async () => {
           initUseRequest({ ...successRequest });
-          await wait(10);
+          await wait(50);
           expect(hook.data).toBe(successResponse.data);
         });
       });
 
-      // FLAKY: https://github.com/elastic/kibana/issues/42561
-      describe.skip('pollIntervalMs', () => {
+      describe('pollIntervalMs', () => {
         it('sends another request after the specified time has elapsed', async () => {
-          initUseRequest({ ...successRequest, pollIntervalMs: 30 });
-          await wait(5);
-          sinon.assert.calledOnce(sendPost);
-
-          await wait(40);
-          sinon.assert.calledTwice(sendPost);
+          initUseRequest({ ...successRequest, pollIntervalMs: 10 });
+          await wait(50);
+          // We just care that multiple requests have been sent out. We don't check the specific
+          // timing because that risks introducing flakiness into the tests, and it's unlikely
+          // we could break the implementation by getting the exact timing wrong.
+          expect(sendPost.callCount).toBeGreaterThan(1);
 
           // We have to manually clean up or else the interval will continue to fire requests,
           // interfering with other tests.
@@ -132,14 +131,14 @@ describe('request lib', () => {
           initUseRequest({ ...successRequest, deserializer });
           sinon.assert.notCalled(deserializer);
 
-          await wait(5);
+          await wait(50);
           sinon.assert.calledOnce(deserializer);
           sinon.assert.calledWith(deserializer, successResponse.data);
         });
 
         it('processes data', async () => {
           initUseRequest({ ...successRequest, deserializer: () => 'intercepted' });
-          await wait(5);
+          await wait(50);
           expect(hook.data).toBe('intercepted');
         });
       });
@@ -152,7 +151,7 @@ describe('request lib', () => {
           expect(hook.isInitialRequest).toBe(true);
 
           hook.sendRequest();
-          await wait(5);
+          await wait(50);
           expect(hook.isInitialRequest).toBe(false);
         });
       });
@@ -162,7 +161,7 @@ describe('request lib', () => {
           initUseRequest({ ...successRequest });
           expect(hook.isLoading).toBe(true);
 
-          await wait(5);
+          await wait(50);
           expect(hook.isLoading).toBe(false);
         });
       });
@@ -170,14 +169,13 @@ describe('request lib', () => {
       describe('error', () => {
         it('surfaces errors from requests', async () => {
           initUseRequest({ ...errorRequest });
-          await wait(10);
+          await wait(50);
           expect(hook.error).toBe(errorResponse);
         });
 
-        // FLAKY: https://github.com/elastic/kibana/issues/42563
-        it.skip('persists while a request is in-flight', async () => {
+        it('persists while a request is in-flight', async () => {
           initUseRequest({ ...errorRequest });
-          await wait(5);
+          await wait(50);
           hook.sendRequest();
           expect(hook.isLoading).toBe(true);
           expect(hook.error).toBe(errorResponse);
@@ -185,7 +183,7 @@ describe('request lib', () => {
 
         it('is undefined when the request is successful', async () => {
           initUseRequest({ ...successRequest });
-          await wait(10);
+          await wait(50);
           expect(hook.isLoading).toBe(false);
           expect(hook.error).toBeUndefined();
         });
@@ -194,30 +192,28 @@ describe('request lib', () => {
       describe('data', () => {
         it('surfaces payloads from requests', async () => {
           initUseRequest({ ...successRequest });
-          await wait(10);
+          await wait(50);
           expect(hook.data).toBe(successResponse.data);
         });
 
         it('persists while a request is in-flight', async () => {
           initUseRequest({ ...successRequest });
-          await wait(5);
+          await wait(50);
           hook.sendRequest();
           expect(hook.isLoading).toBe(true);
           expect(hook.data).toBe(successResponse.data);
         });
 
-        // FLAKY: https://github.com/elastic/kibana/issues/42562
-        it.skip('is undefined when the request fails', async () => {
+        it('is undefined when the request fails', async () => {
           initUseRequest({ ...errorRequest });
-          await wait(10);
+          await wait(50);
           expect(hook.isLoading).toBe(false);
           expect(hook.data).toBeUndefined();
         });
       });
     });
 
-    // FLAKY: https://github.com/elastic/kibana/issues/42225
-    describe.skip('callbacks', () => {
+    describe('callbacks', () => {
       describe('sendRequest', () => {
         it('sends the request', () => {
           initUseRequest({ ...successRequest });
@@ -227,19 +223,26 @@ describe('request lib', () => {
         });
 
         it('resets the pollIntervalMs', async () => {
-          initUseRequest({ ...successRequest, pollIntervalMs: 30 });
-          await wait(5);
-          sinon.assert.calledOnce(sendPost);
+          initUseRequest({ ...successRequest, pollIntervalMs: 800 });
+          await wait(200); // 200ms
+          hook.sendRequest();
+          expect(sendPost.callCount).toBe(2);
 
-          await wait(20);
+          await wait(200); // 400ms
           hook.sendRequest();
 
-          // If the request didn't reset the interval, there would have been three requests sent by now.
-          await wait(20);
-          sinon.assert.calledTwice(sendPost);
+          await wait(200); // 600ms
+          hook.sendRequest();
+
+          await wait(200); // 800ms
+          hook.sendRequest();
+
+          await wait(200); // 1000ms
+          hook.sendRequest();
 
-          await wait(20);
-          sinon.assert.calledThrice(sendPost);
+          // If sendRequest didn't reset the interval, the interval would have triggered another
+          // request by now, and the callCount would be 7.
+          expect(sendPost.callCount).toBe(6);
 
           // We have to manually clean up or else the interval will continue to fire requests,
           // interfering with other tests.