after it times out, try again. i dont know/understand ABE's internal workings, but i'm suspecting its not updating new blocks into its database until it gets a request. then goes away for a time doing the updates.
retries a couple minutes later usually work for me.
if it is NOT running you would get an instant web error, not a time-out.
I've tried quite a few times, but no cigar yet. You could try running abe with the --no-load param, which would avoid the problem you describe. And set up a cron job that runs at a given interval
with the command: python -m Abe.abe --config abe.conf --commit-bytes 100000 --no-serve
It's not that hard setting it up under Apache with fast-cgi either. Which should perform better and increase stability.