A lot of times you see the can/could distinction in conditionals, such as the following:
Type I:
If you
study computer science, you
can become a technical writer.
Type I deals with the concrete, something that is very possible/likely to occur. The verb study is in the
simple present.
Type II:
If you
studied computer science, you
could become a technical writer.
Type II deals with things that are not as concrete, things you might be dreaming of for the future. This involves some speculation. The verb study is in the
simple past.
Type III:
If you
had studied computer science, you
could have become a technical writer.
Type III deals with things that did not happen in the past and the consequences/results. The verb study is in the
past perfect.
Regarding your two examples:
Rejection can happen at any time after surgery; even years later.
How could anyone recover in a hospital?
I find them both awkward.
In the first sentence, I would prefer
may or
might instead of
can.
Rejection
may happen at any time after surgery.
Rejection
might happen at any time after surgery.
For the second, I would make it:
How could
someone recover in a hospital? (talking about a hypothetical situation in the future)
or:
How
can anyone recover in a hospital? (a general question)
If you read up on the three types of conditionals and when to use them, this will start to make more sense.