Many of my clients have chronic mental health problems. Change happens very slowly, and the risk of relapse is high. As a therapist, it can be hard not to feel worn down sometimes, feeling like our efforts are futile. This is particularly the case (at least for me) when clients who have been making progress suddenly relapse, and seem to be back to square one. Whenever one of my clients gets hospitalized, or returns to an addictive behavior - and even sometimes if they're not making progress for what seems like a long period of time - I start to ask myself what I'm doing wrong, or what I could be doing differently, to be a better therapist so that they can get better. Or, at higher levels of care, I feel like the treatment is ineffectual when people need to come back again and again.
This (as I'm sure you've realized) is largely my own countertransference. While there may be a point at which one should question treatment effectiveness, relapse is fairly normal for chronic mental health and addiction issues - after all, change is hard! Negative countertransference when working with these clients is actually pretty normal, too. What matters is how we as therapists manage our countertransference so that it informs but does not negatively influence the work.
A good starting point is giving my ego a reality check: I am not that powerful that whatever I did or didn't do must have caused my client's relapse. I can't save anybody, nor should I. I am a tool for people to work on saving themselves, but a large part of that process is up to them. There are also a lot of other factors in their lives (more significant than I) that influence symptoms - brain and body chemistry, family issues and other psychosocial stressors, etc. Trying to place blame - on myself, the client, or anything else - is not a valid response. A more fruitful response is nonjudgmental curiosity. I want to see what we can all learn from this slip, without implying that anybody should have done something differently this time.
In order to provide this more fruitful response, I need to actively manage whatever negative feelings I have - disappointment, frustration, anger, guilt, etc. I need to do my own work to process these feelings so that they don't leak into my interactions with the client. Supervision or consultation is useful here, or even personal therapy. If a particular population inspires such negative countertransference that management isn't sufficient to turn responses from negative to productive, it might be time to consider a different population (fortunately, the field is so wide that we often do have the opportunity to change populations or settings when we're feeling burned out, or even just bored).
Once I have my responses in check, I have to decide how to proceed with the client. What might my responses tell me about what the client may be experiencing (for example, might my feeling of guilt or sense of failure be a reflection of the client's feeling of guilt or failure?). I also have to decide what, if anything, of my response to share with the client. Might it be beneficial for the client to her how her/his actions affect others, with myself as an example? Sometimes yes, sometimes no. When choosing to self-disclose in this way, it's important to have a clear sense of how sharing is expected to benefit the client, and to review with a supervisor or consultant.
Then, it's good to make self-care a regular practice, including more reliable sources of mastery than therapy!