I did some work on this with the WHO and others almost ten years ago. I speak for myself here.
My recall is that the shift from 110 mm to 115 mm was based on more than one consideration.
The primary consideration was mortality risk. The decision was made on the grounds of both absolute risk and on the rapid change of risk below 115 mm. The "elbow" in the plot of mortality risk by MUAC occurs between 120 mm and 115 mm. This can be seen here:

Since CMAM is a child survival program we wanted high sensitivity as the consequence of missing cases is failure to prevent preventable deaths. This led us to a decision to revise the 110 mm threshold upwards.
We also needed to balance sensitivity and capacity. MUAC is usually normally distributed and small changes in thresholds will lead to large changes in numbers identified. For example, in a population of 10,000 children with a mean MUAC of 140 mm with SD = 14 mm we identify:
MUAC < 110 mm 161 children
MUAC < 115 mm 371 children
MUAC < 120 mm 766 children
Each 5 mm increase in the threshold more than doubles the number of children identified. Selecting 120 mm would have resulted in a c. 500% increase in case numbers. This was too big an increase to argue for at the time for MoH delivered programming. This, and the pattern we saw in the plot (above) caused us to select 115 mm. Some NGOs (e.g. MSF) adopted the 120 mm threshold. Newer intervention models (e.g. COMPAS) use MUAC < 125 mm and vary treatment intensity by MUAC with good results and controlling costs, workloads, and crowding at delivery points.
We could have chosen 116 mm or 117.5 mm but the convention is to use 5 mm steps and this was reflected in the mortality reports available to us. We were wary of squeezing out the middle (i.e. MAM) and had no remit to advise on revising case-definitions.
We could, given sufficient data (now unethical to collect) have selected age-specific thresholds. This would have eliminated the simplicity which is a key feature of MUAC. Also, available evidence showed (and still shows) that adding age or height to MUAC added complication but did not improve case-finding sensitivity or specificity.
Some of the work we did is covered in this report. Note that the recommendation to use proportional weight gain to decide discharge made in this report has already been overturned and MUAC is now used for this purpose.
Following up on Andre's "To my knowledge, no one looked at the curves relating MUAC to risk of death for different age groups. This may not be so easy to do because to look at this you need to break down the population in small subsamples and the association will be subject to a lot of random variation. In absence of effect of a correction for age on risk assessment, I assume the risk should be similar in different age groups". I think:
Briend A, Wojtyniak B, Rowland MGM. Arm circumference and other factors
in children at high risk of death in rural Bangladesh. Lancet 1987; 2(8561):725–8
Vella V, Tomkins A, Ndiku J, Marshal T, Cortinovis I. Anthropometry as a
predictor for mortality among Ugandan children, allowing for socio-economic
variables. Eur J Clin Nutr 1994; 48:189–97.
Briend A, Garenne M, Maire B, Fontaine O, Dieng K. Nutritional status, age and
survival: the muscle mass hypothesis. Eur J Clin Nutr 1989; 43:715–26
Berkley J, Mwangi I, Griffiths K, Ahmed I, Mithwani S, English M, Newton C,
Maitland K. Assessment of severe malnutrition among hospitalized children in
rural Kenya: comparison of weight for height and mid upper arm circumference.
JAMA 2005; 294:591–7
Berkley J, Newton C, Maitland K. Severe malnutrition assessment in children
in rural Kenya. JAMA 2005; 294:2577
Show that the predictive power of MUAC (i.e., the power of predicting mortality) is independent of age even in children below 1 year of age.
I hope this is of some use.