No, a program cannot terminate RRH assistance prematurely, even if the client is not making perceived measurable progress toward sustainability.
The goal should be to help the client meet their self-identified goals even if it doesn't match what the case manager believes is in the client's best interest. However, you may strongly emphasize that assistance is terminating and frankly inform a client that they will likely be homeless again unless they can afford a more sustainable unit.
Once a client has exited from a RRH program, they are on their own, so they will NOT be eligible for new RRH assistance unless they become homeless again. Many clients may not realize that RRH assistance will only become available AFTER they have become homeless again and that they would need to go through the process anew. This may be communicated with clients and strongly emphasized. However, if a client re-entering homelessness is inevitable in the next 3 months, the RRH project may not make that homelessness occur sooner unnecessarily.
Programs may also seek to transfer the client to a different project type which may be a better fit (including PSH if the client was eligible for PSH at entry to RRH). Services should not be deemed as a reward but as an essential life-preserving measure, and sometimes a few more months give the client the time they need to make a plan B.