I believe these stories were first written in the 80's, and the main arc was about soldiers who had been found to have time warping, telepathic and prescient abilities. It was very 'X men' in nature but with a real narrative, taking place in what seemed to be the Vietnam war.
The first story centered around a research project funded by a Government agency that observed (and sometimes sent off to die) these soldiers in order to find the root cause and possibly replicate their abilities. It was inferred that the stress of combat had brought out latent abilities that allow some individuals to become 'super soldiers'.
One story in particular featured a nurse who had a relationship with both the soldiers under observation and the 'lead researcher' who was only looking for results. The nurse herself develops the ability to see into the future.
There were follow on stories about these soldiers and their descendants, taking place in present day and in the future. I believe there were at least half a dozen stories written in Asimov's SF or one of the other paper back short story monthlies.