My team had an issue this morning where the web service went down. At the time, 2 tasks were being reloaded on the publisher server, which is separate from the web server where Access Point and the web service are.
Could these 2 tasks running at the same bring down the web service or is the amount of users logged on at that time the issue?
I doubt that the fact that two tasks are running at the same time is what brought the service down because it's pretty common to run multiple tasks simultaneously (we normally run four, sometimes more at the same time).
You should check the Web Server log to see if you can find anything unusual that might caused the service interruption. How many logged users does the server has at a given time?