if a nanny lost your house keys, would you expect her to pay to replace them?

[Tutter]

and would you be pissed off, or just see it as One Of Those Things?

No I wouldn't

Anyone can lose a key!

No to cost of replacing - Yes to being pissed off. What will they lose next, a child?
I think that the circumstances surrounding the loss is more important, was it lost due to carelessness, due to faulty equipment (i.e. keyring), or some other factor. Given the importance of a work key, most employees I would have thought would look after a key like it was gold.