Nope, if you have tracking which has shown delivery then if she opens a case you enter the tracking details, and the case closes in your favour.
Tip, always enter that tracking or 16 digit number from your proof of posting straight after you have marked the item as dispatched. Then, if a case is opened and the numbers have proved delivery it closes within 24 hours in your favour.
You can politely message the buyer that it does not have to be the signature of the recipient on delivery. posties are allowd to sign themselves once the item has been delivered.
Have they asked household members / neighbours if they took in the item. Ask the postie if they remember which 'safe' place around the house they left the item.
