analogue for "infantilize" at the other end of life
As children grow you should be careful not to infantilize them when they may need some help - it's important to let them struggle with things they are just becoming capable of, so that they become more capable.
When helping someone at the other end of life it's important not to help them so much that they lose life skills more quickly than they might if they were allowed to struggle some.
Is there a word (or short phrase) for what you shouldn't do? Senilitize doesn't seem to exist.
While "infant" is visibly within the term "infantilize," the term is not only applicable to young children.
Infantilize is just a baby, relatively speaking, in the English language family. It first saw the light of day in the early 1940s, when social scientists started using it to discuss ways that humans or human activity can prolong or encourage dependency in other humans by treating them as helpless. The adjective "infantile," which gave birth to "infantilize," is far more mature, however - it's over 300 years old. "Infantile" sometimes literally means "relating to infants" - that is, to children in the first year of life - but it also has a broader meaning; if I chide someone for his or her infantile behavior I simply mean that the person is acting immature or childish.
Source: http://www.merriam-webster.com/dictionary/infantilize
It would be possible to "act as if someone were dead already," but usually that turn of phrase is taken as being dramatic and/or offensive. There are words which are more general, but again, they are not necessarily age-specific: to enable someone (in a negative way)1, to baby someone, to serve as a crutch, to coddle, to pamper, etc.
You may not find any word specifically meaning: to treat someone as if they had lost capacity and were close to death, because such things are somewhat taboo -- at least in U.S. culture. I can't speak to how things are in other English-speaking countries, and there may be words to describe such things elsewhere. But, those mentioned above are the only ones I've heard used here.
"overprotect" or "be overprotective" seem to fit.
"When helping someone at the other end of life it's important not to overprotect them that they lose life skills more quickly than they might..."
overprotect - to protect too much; coddle. TFD
"reach dependency" or "become dependent" also come to mind.
"...at the other end of life it's important not to help them reach dependency/become dependent so much that they lose life skills more quickly than they might do otherwise."
dependent - "relying on or requiring the aid or support of another:adult children who are still dependent on their parents." TFD
dependency - noun - "the state of being dependent"