I face the same problem:

sp_cycle_agent_errorlog works fine some time and then it stops.

This occours on any configuration (SQL 2008, 2012, clustered, non-clustered, ...)

The cause is as you described: SQL Agent doesn't release it's file handle. Restarting the SQL Agent Service solves the Problem - for the next weeks :crazy:

sp_cycle_errorlog allways works fine 🙂

Did anyone figure out how to fix this permanently?