It seems there's an underlying conflict with MS OS and Adobe Digital Editions 4.5.9., i.e., Windows seems to disregard the ADE.exe file after upgrading to ADE 4.5.9., as it won't display it as an available application in the File Association window even though it lists it in the Default Apps list. There's loads of traffic on the internet about this and nobody seems to have found a solution yet - Adobe are markedly silent on this topic! But I discovered a workround that worked for me and I thought I'd share it to see others find it helpful. Note: I'm using Windows 10, so can't comment on whether this work round will work on other Window versions.
Hope this helps.
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Further to my original post, I just wanted to clarify that it seems this issue is not an Adobe issue: I've just applied the latest update to my Windows 10 Home system and the issue has been cured!