I have no problems rendering with AE in the background while doing other stuff. Depending on the complexity of the project and priorization of threads it might be slower than when in focus but that largely depends on your system settings, your CPU(s), GPU (when dealing with certain GPU accelerated effects) and of course what you are doing while your project is rendering. Reading a textfile might take less resources from AE than surfing, streaming or running complex physic simulations. So to sum it all up, you provide too little information to comment on your issue.
AE renders in the background for me on my Mac. If I'm doing a lot of other things, actually, almost all the time I use Adobe Media encoder for rendering so I can work on other projects with AE or other apps while the render is processing. If you are rendering compressed formats for delivery AME is the preferred rendering option anyway. You'll get better quality. There is only a slight speed improvement rendering production formats from the render cue for most projects because only a few plug-ins take advantage of AE's ability to render multiple frames simultaneously.
I think there must be something wrong with how the default configurations are working with my machine. I merely need to switch to another program, text edit, Firefox, or photoshop with an undemanding file and then I hear the After Effects 'render complete' sound after a couple of seconds and there it is thinking it's finished when it's just given up.
I'm running 16Gb Ram and a 240GB SSD drive, not tons of disk space, but as I say, it's fine when the program is in foreground
The project itself isn't massively taxing in AE either, mostly transforms and zooms with some transparency overlays.
Is there a log file I can submit or something?