Would muscle fatigue still occur if aerobic conditions for a working muscle is maintained?
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:


Godwits have been recorded flying over 7000 miles (>11000 km) without stopping for 9 days
Arctic terms migrate 44000 miles (>70000 km), albeit with stopovers
Humpback whales migrate 5000 miles (8000 km). Their muscles are probably operating close to continuously.
Many (most?) species of sharks swim continuously.


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).
Race Across America, Paris-Brest-Paris, and similar endurance bicycle races. The RAAM has a record time of 3107 mi (4971 km) in 8 days, 9 hours for a mean velocity of 15.4 mi/hr (24.6 km/hr).