As Natali said, we can't possibly know what's going on with Jake. And honestly, it's not our right to know. I know no one here is saying that it is - just thinking out loud.
Heath was extremely private. Jake is known to be fairly private, too. In any event, neither of them has ever owed us, the fans, an explanation for anything they do (or don't do).
I kind of think some folks are transferring some of Ennis and Jack's relationship onto Heath and Jake, and understandably - their portrayals were so honest and real, it's hard not to believe that they have a very similar relationship in real life. I'm sure Jake cared very much about Heath, and for all we know, was still in frequent contact with him. They worked very closely together for a significant period of time and forged a bond - I'm sure time and distance hasn't done much to sever that. That said, just because Jake happened to costar as Heath's character's lover in a movie does not require him to make a statement. Sienna Miller did that fairly recently, too. Has she made a statement? Christian Bale and Maggie Gyllenhaal have very recently costarred with him. Have they made statements? Is anyone upset that they haven't? It's each person's choice, and I don't think it's fair to judge someone who worked closely with him and considered him a friend but has opted not to make a statement at this time unless we're judging all of them the same.