They should contact you but whose responsibilty is it? Yours or theirs? If a small item such as keys,cellphone (who isn't on it already) or wallet (you will need it within the hour) is lost well then people should contact the hotel,and not wait for someone to eventually hand it over to management.

The policy is way to long (30-90 days),but by then the item was not really important.

I for one left a pair of jeans and I noticed it a day later,asked the front desk about it and they did have the item,they shipped it for me,but was not home to accept it,they called me again and said they wouldn't ship,or I can donate it,I decided for them to donate it (regardless if their staff kept it or gave it to someone).