@gollum,
Call them up again. Ask to speak to the facility administrator's office. Relay the history of the requests. Tell them you are giving them until (a reasonable date in the near future) to retrieve the chair. After that, you will not be responsible for their property and will give it to a charity/person that can use it.
If you wanted to, you could do that by mail so you have a record of your notification should they attempt to recover money from you.
Speaking of money, you might check the bill you received or that was sent to your insurance company. Chances are that you or the insurance company were charged for the chair and the chair is, in fact, already yours.