I don't have family sharing and I don't use more than one device.
Thank you for clearing that up. That was an unknown possibility. If your answer were different, then it might have been a solution.
As I said, I deleted all the previously downloaded episodes. All I can download now is one show before I get an alert saying I've reached the download limit.
Apple’s description on the support page suggests that the maximum number depends on the Channel, such that each content provider can heave their own limit. Did your contact with Apple or HBO reveal what the subscription limit for HBO downloads through Apple TV app Channels is supposed to be?
I'm sorry to be snarky, but I have called Apple support and they couldn't fix the problem. They told me to call HBO. When I called HBO they couldn't fix the problem either and told me to call Apple.
Sorry to hear that they’re pointing at each other. The formal answer may need to come from one of them … By that I mean how the number of downloads is being kept track of, and how to reset the counter, to get the full amount again.
I depend on offline viewing.
Offline viewing has been one of the perks of Apple TV app Channels, so I find it very understandable that you would want to make use of that.