Is it possible for life to continue and be sustained without evolution?

In the simplest terms, evolution is synonymous with change. Life without change is stagnation; stagnation is the first step on the journey to death.

Try it this way: one of the least avoidable laws of nature and physics is entropy. It cannot be delayed, it cannot be denied. Entropy is change, and is likely a huge component of evolution.

So, short answer, no. Life would end without evolution.