When it gets too hard to work you may want to switch to a juice fast/feast for a while. When we fast with water only our bodies are living off of our diseased tissue. If you take tea this is sabotaged and you stand in danger of entering a starvation mode. When you switch to juice you will be living off of the juice and not your body, but it may be the break you need to get back to successful water fasting.
If you need the tea for a day or two to help you get started I don't think it would be any big deal, but you do not want to continue Water Fasting with a cup of tea occasionally.