Why do humans lose subcutaneous fat tissue with age?
Short answer
We do not loose fat (cells) as we age; on the contrary - we tend to gain fat by about 1 or 2% per decade. The place where it gets stored does change; instead of going into subcutaneous regions, it gets stored around the abdomen. A sex hormone imbalance might be the cause of this gain in visceral fat. 

Background
What a coincidence! I just finished an article in the Sci Am May issue of this year (2018) on exactly this topic, literally just minutes ago. 

In young folks, fat tends to accumulate under the skin, while in older folks this tends to shift to accumulation of fat around the abdominal viscera (the internal organs). Bottom line: we don't loose fat overall, we just store it elsewhere. What's more, as we age we store more fat as our base metabolic rates drop.  

Why this happens is no known, but there are some interesting findings:


Sex hormones are involved; women in menopause (estrogen levels drop) gain more visceral and belly fat and loose it around the hips (they go from pear to apple);
However, a drop in estrogen is not the cause, as certain ailments lead to belly fat in young women with plenty of estrogen;
Androgen-using females (transgenders) gain more visceral fat.


These findings together have lead to the idea that a sex hormone imbalance might be the cause. However, some findings counter this idea:


Afro-Americans have less visceral fat, while Asians have more;
Blocking FSH results in less visceral fat, which may have other mechanisms of actions than estrogen.


Reference
- Wallis, Sci Am May issue 2018