This is one article in the larger Troubleshooting SharePoint Alerts guide

Problem

Task, Project Task and Issues lists have a “Send e-mail when ownership is assigned” feature.

When you use Item-level Permissions and set Read Access to Only their own these emails no longer work.

You can't select both Read Access = Only their own and "Send email when ownership is assigned"

It appears that when you go back to Settings > Advanced Settings the Send Email when Ownership is assigned radio is set back to No when using Read Access = Only their own.

Why

Speculating here – I think that its because its very possible to set this up so the owner is not the assigned to person so you shouldn’t send an email to someone who shouldn’t be able to read it (and remember that when you re-assign a task an email goes out to both the old assignee and the new assignee) so rather than deal with these tricky scenario they just decided to disable it altogether.

Verified with

WSS3.0 12.0.0.6535 (SP2 + April 10th Cum Update)

References

• Assigned to email stops working when item level permissions

Related posts:

1. Troubleshooting SharePoint email alerts – Checking the Email Infrastructure This part of the alert troubleshooting guide will talk...
2. Troubleshooting SharePoint Alerts – User List and List Permissions This part of the Troubleshooting SharePoint Email Alerts guide...
3. Troubleshooting – Task modified alerts getting sent to random, incorrect recipients This is one article in the larger Troubleshooting SharePoint...
4. Troubleshooting – The url in Alert Email is incorrect This is one article in the larger Troubleshooting SharePoint...