I have also seen something similar when we were using 32-bit SSAS and this stopped happening when we moved to 64-bit SSAS and the extra RAM that came with it

I'd say that 8Gb of Ram is a very modest amount especially if you are using SQL Server & SSAS (& the OS) on the same server

Have you got a spare SSAS server? Maybe try turning SSAS off on you problem server and try processing the cube on a spare server pointing to your problem server's SQL instance

Mack