B737 Captain reported engine cowl anti-ice caution light during cruise. The crew continued to the destination and landed safely.

Narrative

We were cruising at flight level 340 from ZZZ1 to ZZZ when we got a number two engine Cowl anti-ice caution light. We accomplished the checklist which told us to reduce the power until the light extinguished. We reduced to the power all the way to idle; and it did not extinguish. With the power at idle on the number two engine; we were unable to maintain altitude; so we accomplished the drift down checklist; and I called ATC to descend to flight level 240. As per the checklist; we contacted dispatch and Maintenance Control immediately. Maintenance Control had us check the circuit breaker and recycle The Cowl anti-ice valve; but that did not solve the problem. Maintenance Control informed us that it was OK to continue on to ZZZ; so that's what we decided to do after some discussion between myself and the first officer. We were both comfortable with that since the engine was still running and we could use it if needed. I [requested assistance] with air traffic control and gave them our souls on board and fuel remaining. I wasn't sure if we would have any further issues and thought this was the best course of action. We continued on to ZZZ and landed with no further issues.