How long did it take for his family to come and collect his belongings? As long as his stuff is still in the home, he (his estate) is still technically responsible for the rent. Even though he himself is deceased and no longer physically living there, it's not like you can rent it out to anyone else while his stuff is there. Was there any sort of rental agreement? If there was any sort of "notice to vacate" clause, then you'd also be within your rights to keep the money as well.
It's probably up to you though, if his family are demanding a refund - and you can afford to be generous, you could give a prorated amount back, provided that they come and remove his personal belongings ASAP. Otherwise, despite the sad occurrence, I don't think that you are legally obligated to refund anything (though that could depend on what state you are in as well).
I agree with the above statement. Unless family closes on the estate and has stuff out of there before end of month, no refund is justified. You can prorate a refund if they collect items before end of month.