The problem is being open costs money. In order to be profitable, you need to bring in more money than the cost of the labor, and that's after you account for cost of the product and the other fixed costs.
There is also the trouble that most of the people who will be around at close of business likely came in an hour or two earlier, so you are essentially paying someone to monitor the cafe without bringing in any new revenue.
I would think the morning before-work rush would be the best time to capture money as a coffee shop, same with the after work time. They are basically only open while working people are away from the neighbourhood and have their doors shut when the biggest rushes of people would be there.
And it's not just them, I see a lot of local businesses in this area struggling, but the problem is they aren't open to take my money at reasonable times. There's another café even closer to me that is trying to make it, but they are closed 2 days a week and it's not the weekend, I'm not sure which days they are, so it's hard to check it out. It's just baffling to me - you pay rent 24/7, you have bills every month, and staff … but if you want to take money (generate income) you have to be open. If you want to make the most money, shouldn't you try to have your doors open the most amount of time you can?
The coffee shop closest to my house has the same problem. The only times they are open are while I'm at work. They opened right about the time we moved (a little over a year ago), and we were excited to have a play we could go close by. But they are never open when it would be convenient for us.
The dumbest thing in my mind is that they are open for like 4 hours on Saturday (7am - 11am).
I think the problem with that particular coffee shop though is that they lady who owns it also runs a catering / event hosting business, so the needs of the coffee shop come last.
There is also the trouble that most of the people who will be around at close of business likely came in an hour or two earlier, so you are essentially paying someone to monitor the cafe without bringing in any new revenue.