OK I'm VERY new to this (been a Telltale player for years, but only just downloaded Walking Dead - been reading the books since the start, and love the show, and love gaming on the iPad so decided I'd grab this, especially being free at the moment for ep 1), and I realise many people are having these issues, and have been for a long time, so I apologise if I'm covering old ground etc.
SKIP TO THE LAST PARAGRAPH if you don't want to read how I came to my successful conclusion.
I've seen many posts here about problems downloading the DLC. I bought all 4 extra eps on the strength of what little of ep 1 I've played, and thought I'd download them in advance so they're ready when I get to them.
Now my iPad (4th gen) has no SIM (to avoid unexpected/excess data charges from my provider). I can tether using my iPhone but I almost always just use wifi (considering work, home, inlaws etc all have one, why not).
Using my (strong signal) work wifi, it took 1.5 hrs to get to 99%, and stuck there for longer than each percentage point had taken up til then.
Considering all the posts here about the download hanging at this point, often for hours (despite TT's assurance in the sticky at the top that this was fixed) I quit the app (whilst I don't get charged for work's wifi, why waste my time?).
Started it again, after noticing someone's post saying the download picked up where it left off, but mine didn't... 0% again... stuff that!
Anyway, came home, put my iPad on charge (wondering if that might help), and started the d/l of ep 2 again... 'connection failed/interrupted' or whatever the message is, before progress had even proceeded past 0.00% (after which it should become 0%, then 1% etc).
During these attempts of course you're never sure if TT might be actively doing something with their servers at the time. I thought since this behaviour was different to what I'd seen earlier (my wifi signal at home is stronger than work's) I assumed maybe they were doing something, but thought last thing I can try is to put the iPad right next to my wireless router.
Wow. 1% every 3 seconds. The download hit (and passed) 99% in barely 5 mins. 'Installed' appeared. Hallelujah, I thought (and I'm an atheist!).
Ep 3, same thing.
So... after all that, and notwithstanding how long this has been an issue for many people, I thought I might just drop by and suggest that if you have an in-place wireless network and are still having trouble downloading DLC, try putting the iOS device right next to the router, for the strongest possible signal (and consequently minimal chance of signal fluctuations messing things up). It worked perfectly for me; all 4 additional eps downloaded within 15-20 mins.