They appear to leave Henry home alone to lounge around Reba’s house multiple times a day. And didn't Reba finally point it out one day and they panic and run home?

^^^ They did leave Henry at their house alone during the season three episode when they learn that Kyra was sneaking over to Reba's house in the middle of the night just to get away from the fighting that went on at her dad's house.

God bless you always!!!

Holly

P.S. To answer the question, are they irresponsible? In my opinion, the only responsible person on the show may have been Kyra.