I see a similar issue. Smaller recorded shows, about an hour, download ok. Larger files, say 2 or 3 hours and up, download to 80% - 90% and then starts the download over. I'm putting these on an iPad and have over 100GB free. I don't think it's a space issue. I have the latest IOS version 10.3.3 and my iPad Pro is pretty new.
I wonder if there's a timeout built into the Stream Tv app??
I'm doing this on a wifi. According to the Speed Test app I have 117 Mbps download and 111 Mbps up.
I am not sure how large the bigger (longer) recordings are however. I checked my storage before and after a one hour show download. For Stream Tv it went up about 1GB. Did the check twice and 1GB is in the ballpark. It took about 3 minutes and 10 seconds to download.
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