"Lost" NHS pension

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I worked from 1979 to 1986 and paid into the nhs superannuation. I did not withdraw this money but now that I am 60 (this is the age I can draw my very small pension) the NHS pensions cannot find it and I presume I cannot be paid. I have given all the details I have including NI number to the pensions department but I have not retained any payslips.
Has anyone experienced this unfairness?

If you left the employer between April 1975 and April 1988, you will have a pension, provided, you were over age 26 and had completed five years in the scheme. If not, you will almost certainly have had a refund of your pension contributions and have no further rights.
Try
www.gov.uk/find-pension-contact-details

The NHS pension scheme is administered by the NHSBA and the OP has been in touch with them so I don't think she needs to track them down, it's that they have no record of her contributions. They should have records of all scheme members going back that far (they have mine going back to 1979) but something has obviously gone very wrong in your case OP. As has been said, obtaining a statement of NI contributions may help as the NHS scheme was contracted out and the fact she was contracted out should be indicated on her statement.

Update:
I have found my pension. I worked in Scotland for the last 18 months of my NHS working life. I woke up today and wondered if I could attack the problem "backwards" by contacting the SPPA. I did and they were so helpful. They found my superannuation number within minutes and using that were able to locate my English pension. I have no figures and have to send in a long form but in 3 months I should have a very small pension backdated to my 60th birthday.
The English equivalent were spectacularly unhelpful although I realise that they have a larger, and probably more mobile population to deal with.
My success was down to chance and I think this is still an issue for many people.