Once the user is logged into the phone, it resets itself after up to 10 minutes and logs out of Extension Mobility (EM) automatically.
The maximum log in time is configured to seven hours and 59 minutes, so it was not causing the problem.
An EM trace showed EM users logging in, but it does not show them logging out.
The issue was that the clock on the subscriber was one day ahead of publisher. More specifically, it was the maximum log in time ahead of the publisher, which is eight hours by default.
To resolve this issue, correct the time on the subscriber and reboot.