Can a muscle fatigue after 2-3min work, at sub-maximal loads? Indeed it can. 

Muscle fatigue can be predicted by the tension time index (TTdi), a tool developed by Clanton & Grassino in the 1980’s. A tension-time index of 0.15 can predict fatigue when a muscle works indefinitely. The TTdi is the product of normalised force * contraction time/contraction-relaxation time. In our performance laboratory, we have demonstrated trapezius muscle fatigue following three minutes of isometric contraction with 30%MVC. We did this by developing a TTdi for this muscle.

For example, a contraction/relaxation cycle lasting 20s (with 12s contraction, and 8s relaxation) produces a ratio of 12/20 0r 0.6. When we work at 30%MVC (0.3), we can use the equation above to develop a TTdi for this scenario. This becomes:

0.6 * 0.3 = 0.18

As stated above, a TTdi of 0.15 is predictive of muscle fatigue.