He's had a couple years right at .300, but other than that he's hit .260s or .270s most seasons of his career (Career average at .280). Guys that regularly hit .300+ tend to be less streaky than guys like him. So this could be a bad start. He still could end up hitting mid-.260s with 30+ HR this year.
As far as the age goes, typically as guys hit their mid-30s their power will stay a couple years longer after their batting average begins to drop off. However, usually guys with better averages to begin with can take the 30-40 point drop in BA and still be productive hitters, while the Andruw Jones' of the world become very worthless, very fast when age catches up to them. Delgado seemingly played 162 games every year there for 5-6 years, with over 1700 GP so far. Those extra games could wear on him and make him show his age earlier.
So basically it's reasonable for him to come back and this just have been a slump, but it's also reasonable for him to be toast. Right now it's probably more of a gut feeling for you than anything. One thing to think about is the fact that you won't get anything good for him right now, so you probably can't trade him. Special fun for you. Congrats!