Timing.... there's probably some test step execution being attempted before the object is fully resolved/rendered on screen or the page hasn't completely loaded. Issues like this I've seen occur more frequently when tests are running for a while against an application, especially as the application starts caching more memory.
Take a look at the steps where the error is happening and make sure that you have all the necessary "Wait" calls and such added to have the automation be "smart".
Another thing... is this a web application? And is there a difference in environment between running them one-by-one versus running them in batch? The reason being is that, while TestComplete is pretty good at making sure it scrolls components onto screen before it attempts to execute an action, it's not always successful. We've occasionally needed to add a call on components of 'scrollIntoView(true)' to make sure that we scroll the component into view on screen before we attempt to execute a test step. That's something else to investigate
