This is a very interesting question. At first glance, one might be tempted to say that medical advances in order to heal people are crucial. After all, is it not our moral responsibility to look after each other and help each other? However, as you point out in your question,...
This is a very interesting question. At first glance, one might be tempted to say that medical advances in order to heal people are crucial. After all, is it not our moral responsibility to look after each other and help each other? However, as you point out in your question, this leads to a totally different problem. If illness and disease decrease within a society, then people within this society will become much older than they would have become otherwise. Retirement homes and care homes are already struggling, as there is such a demand for them, given the vast number of people in need of care in old age. However, there is often not sufficient money to fund it.
One of the ways to solve this would be to increase the amount of money people have to put into their pensions before they can retire. As people are now expected to live much longer, the current amount of payment that goes into pensions is simply not sufficient.
Eliminating retirement completely would be a very inhumane solution, as this would create a society where people are expected to merely live in order to work. Older people would be expected to work until they literally die on the job. Would life still be enjoyable for humans at this point? Or would this merely turn humans into machines?
Another issue with continuing to work is that some jobs are very physically demanding, such as the job of a firefighter or a policeman. An elderly person may simply not be physically able to keep working in this job. In fact, an elderly person in such a position might even turn into a liability.
A good compromise might therefore be to delay retirement by a few years but to combine this delay with support for older people and the establishment of suitable jobs for their age group. In doing so, people, who would normally enter retirement age could be requested to keep working for another few years in order to increase their pension payments to a suitable amount to cover their retirement costs. However, rather than continuing in their usual jobs, these people could be transferred to jobs which are particularly reserved for the elderly, in order to ensure that they are not too physically demanding.