Has anyone here had the experience of successfully applying to study the same masters degree that they once failed, based on changed circumstances? If so, did you manage to study at the same institution?

You have to ask yourself what did you wrong? But the key question is "was that Masters right for me?" There are plenty of Masters which might be similar to the one you chose, that maybe a better fit. You need to sit down with the Course Co-ordinator (Department Leader) talk to them and ask serious questions regarding the course. Didn't you get interviewed and talk to the course leader?

Thanks.
I couldn't finish mine due to money matters which led me to become depressed, and I had no information at the time that I could withdraw etc. My university didn't advise me that way and went ahead and failed me even though it knew what my situation was. Things have improved for me since [five or so years later] and I want to do the same degree but don't know how my application will be received. So, any examples of success in trying again would give me hope.

Abiart, I feel your pain I was suspended from University for 1 month before I was to finish my final modules (exams) for non payment (funding was delayed). Try doing a presentation for your final project without a University log in. You best bet is to explain this to the course co-ordinator and if you have a transcript show them, I was fortunate as I explained my situation to the Course Leader and Module Leader, they explained I would only be penalised for 1 module and not my final module. All I can say is talk to them, you won't be the first or last.