I've left a few items in hotel rooms. I've always recovered them after I inquired, though my mileage in each case did vary:

Once it was a set of 4 shirts I left rolled in the closet. Getting those was easy as I returned to the hotel less than 2 hours after leaving, and the room hadn't yet been serviced.

Another time I left my electric shaver in the bathroom. When I called the hotel, they confirmed it had been turned in and asked me how I'd like to get it. I asked if they could ship it to me, using my credit card on file, and charge me the actual shipping cost plus a reasonable handling fee. The hotel manager (whom I was already speaking to on the phone) agreed. But then their turnaround with shipping with slower than I expected, so for next-day shipping cost I got it 3 days later.

The most dramatic recovery was of a stuffed animal that has enormous sentimental value to a family member. It got left on the bed when we checked out. I phoned the hotel several times that day, speaking to multiple staff members including the housekeeping manager, who all swore they checked the room and/or checked with housekeeping and couldn't find it. Finally on about my 5th call, I was speaking to the hotel manager and pleaded my case: that a child was had been sobbing for hours over an irreplaceable loss, that I was the villain (it was "my" responsibility not to leave that stuffed animal under a bed sheet), and couldn't she help me be the hero and restore peace to my family? She made one extra effort, and sure enough there it was: the stuffed animal had already gone through the laundry with the sheets and was sitting on a shelf in the laundry room. I drove back to the hotel, about an hour out of my way, to collect it.