I running 64 bit Eclipse (both 3.6 and 3.7) on 64-bit Windows, and the m2e plugin (which provides Maven support) installed and works just fine. I installed m2e from the Eclipse marketplace. The plugin itself does not have any non-Java components so it should just work with both 32-bit and 64-bit versions of Eclipse.
Exactly what is not working? It would help if you detailed exactly what you are doing and what problems you are seeing.
Also, how did you go from 3.6.1 to 3.6.2? By doing an upgrade within Eclipse? I have found that upgrades tend to fail on me way too often so I avoid them. Instead, I grab the new version and install it in a new location.
The problem is that I cannot come to you and watch over your shoulder as you do things. If I could do that, I could help you. But since I cannot do that, you have to describe in detail what it is you are doing and what you are seeing. If you cannot do that, then I cannot help you.
When you originally wrote about permission errors, I imagined file permission errors. But these are web site permission errors. To prevent such misunderstandings in the future, always post the exact text of the error message(s).
For some reason, you are being blocked from accessing the web sites for the plugins. Here are some things to look into:
a) Can you access the URLs given in the error messages using a browser?
b) Is there are firewall blocking your access? This can happen in a corporate environment.
c) Are you using a proxy server to access the internet?
Then there is an issue with the 64-bit JVM that you are using to run Eclipse. Either that, or there is an issue with the 64-bit Windows winsock DLL (which the JVM uses to perform internet access). You could try running the 64-bit version of IE and see if that will let you access the URLs. If you can, that eliminates the winsock DLL as the issue.
Please post the results of "java -version" for both your 32-bit and 64-bit JVMs.
You should also run Process Explorer from sysinternals and check which DLLs are being loaded for each JVM. Perhaps something there will tell us what the issue is. If you are not sure, you could post the DLL list and I could compare with mine.