Tony's light had flickered out in the aftermath of the fight with the Chitauri, but his team was there and, hey, he'd just been to space, give a guy some slack. The next morning they accepted, but when he collapses weeks later, they're not going to let him brush it off again, and neither is JARVIS.
Illness is a private affair, one that Tony deals with as effectively as he always deals with self-care - as in, not at all. He sends pretty much everyone who looks for him during his times of sickness into mild or major panic, depending.
The arc reactor, despite being a technical marvel, is quite invasive. There have to be side effects to its presence in Tony's chest beyond the now-resolved Palladium poisoning. The team are about to find out just how debilitating it can be. This would be easier if Tony didn't feel the compulsion to hide the fact that he's sick. Misunderstandings all around, especially given Stark's reputation.