Kathleen Thompson, 47, was shot dead in the back garden of her home during an Army search operation at a neighbour’s house in the city’s Creggan area.
A fresh inquest into the death of the mother of six started in 2018.
It heard in 2019 that there were as many as 350 potential soldier witnesses.
The proceedings are one of a number of inquests ordered into deaths from the Troubles which are being heard.
A preliminary hearing on Wednesday heard that witness KTM 7 had responded with medical information, but had not responded to further contact attempts.
Witnesses referred to in court as KTM 120 and KTM 986 were also heard to have presented with medical issues.
The coroner, Judge Sandra Crawford, asked the Ministry of Defence for updated information regarding the position of those witnesses.
The coroner’s court also heard that a letter from a GP had been received in respect of witness KTM 220 which described “significant health problems that in his opinion will very substantially impact on his ability to give evidence”.However, Andrew Moriarty, for the next of kin, queried whether the letter was sufficient to excuse the witness.
“In that letter the general practitioner states as follows, ‘he would be unable to provide useful information around the events as he would not be able to recall reliably’,” he said.
“I would simply make the observation that whether he can provide useful information or whether he is able to recall the relevant events reliably, these are matters for the court and I don’t really think that the general practitioners’ letter particularly passes muster if one is considering not pursuing KTM 220.”
Judge Crawford responded: “The issue of whether the information that has been provided is sufficient will be one of the issues that I will consider and we will return to that matter on the next occasion.”
A further preliminary hearing is set to take place next Wednesday, May 12.