When AccuRender begins a rendering, it has to allocate a large block of memory to hold the finished image. If the rendering you are attempting is big enough, Windows may not be able to allocate that much RAM.
The amount of memory required by AccuRender depends on which image channels it is writing. By default, AccuRender will write 3 color channels, luminance data, a distance channel, material ID channel and an alpha channel. The last 3 of these can be turned off on the Render Settings dialog.
The solution:
If you need to render an image and AccuRender reports that it is out of memory when you press the Render button, please turn off the Distance, Material ID and Alpha channels and try again.