Bethesda gets asked about Fallout 4 a lot. Probably too much. It's safe to say they're pretty sick of it at this point.
Pete Hines, as the main spokesperson for the company, gets a lot of these questions. For example, earlier this week he was asked whether Fallout 4 would be making an appearance at E3. He, predictably, shot down that gossip:
The most solid information we have about Fallout 4 comes from last year's leaked casting documents. Those documents suggested that the game will take place in the Boston, Massachusetts area. The region, which became the Commonwealth after the nuclear apocalypse, was referenced several times in Fallout 3 and its DLC. That leak, like the petition, was met with silence.
At this point, I think Bethesda's proven that they're not going to be swayed to make a Fallout 4 announcement before they're ready to do so. It doesn't matter what's been leaked about the game or how many fans ask them. Another tweet in Hines' direction isn't going to tip the balance. The company's made it clear that they're still a long way from talking about the game.
Granted, Fallout 4 seems like an absolute certainty and Bethesda wouldn't be giving up much by admitting that certainty. It would be like Rockstar announcing that there's going to be a GTA 6 or Valve that there's going to be a Half-Life 3. It's amusing how far these companies will go not to confirm these inevitable sequels.
Look at it this way, though: would you be even remotely satisfied by a tweet confirming that Fallout 4 is in development? It would do absolutely nothing for me, and I'm someone who loves the crap out of Fallout. I don't think anyone aware of the sales and reviews of Fallout 3 and Fallout: New Vegas has any doubt that a new game will be coming eventually. Getting a simple nod from Bethesda without any other details wouldn't be gratifying at all. Either way, the wait for a full reveal goes on.