New/updated annotation icon highly variable in how long it takes to appear

**Describe the bug**
Unsure if this is related to https://github.com/hypothesis/support/issues/99.

A user has reported that the red new/updated annotation icon is not appearing for her. I can not replicate this, but I do see intermittent long delays in the icon appearing which may lead to someone believing the icon did not display. There do not seem to be special steps to make this happen.

**To Reproduce**
Steps to reproduce the behavior:
1. Open the LMS app as an instructor, and in another browser (or incognito window) as a student
2. Open the same assignment in both windows
3. Leave annotations as both personas
4. Time how long it takes for the red icon to appear.

In the attached video I make both annotations in the first 13 seconds. The student window (left) gets the new/updated annotation icon at approximately 2:24. The instructor window (right) gets the new/updated annotation icon at approximately 18:22.

**Expected behavior**
To be useful in class, the icon should probably appear within a minute or so of the annotation being posted.

**Video**
Here: https://drive.google.com/file/d/1IxCJO9PVVP_cvyk_MZOx1CeEOESg1NfU/view?usp=sharing

**Desktop (please complete the following information):**
- Mojave 10.14
- Chrome 85

**Additional context**
https://hypothesis.zendesk.com/agent/tickets/12787
https://hypothesis.zendesk.com/agent/tickets/13112