Put another way if the muscle is given everything it needs to contract and do work will it ever get tired or have a reduction in energy efficiency?
As far as I understand muscles depend upon a blood supply delivering oxygen and nutrients (e.g. glucose and calcium) to effectively contract at its best level of performance. With the ability to work under anaerobic conditions if need be but producing lactic acid as a by-product which reduces the muscles ability to contract and therefore producing fatigue.
I also know that muscles are dependent upon temperature to work efficiently like the rest of the body. So, if the muscles temperature was able to be regulated well enough to maintain efficiency and aerobic conditions are met could fatigue be negated?
It seems that you are asking about activity significantly above basal metabolic rate. If aerobic conditions are maintained (and with appropriate training), muscles can operate more or less continuously for very long durations, days to weeks. In non-humans:
There are probably other examples as well (feel free to add). For humans, usually the limit to endurance is sleep. Two forms of racing push human endurance, but the longer races almost always require at least minimal sleep:
Ultramarathons, foot races of 50 mi (80 km), 100 mi (160 km) or more (e.g., 24 hours, multi-day).
If the muscle is provided with adequate food and oxygen, the muscle can theoretically work indefinitely. However, microtearing when a muscle is stressed more than usual can over time damage the muscle. This is the mechanism by which you get larger, stronger muscles. Without rest, it's theoretically possible to simply destroy the muscle faster than it can be repaired.