I have tried twice using Twitter direct messaging and last time it was over 4 days before I got a response. The most recent messages again 4 days ago to get some answers and as of this post no response yet, imagine that! It is my suggestion that you stop using auto response on @Visblecare telling everyone to direct message on that platform when no one is responding to those DM's. Maybe it is just mine being ignored.
Now for Facebook messenger. The messages I sent on Twitter 2 weeks ago I had sent a day earlier on FB and after 5 days someone finally responded there, it happened to be the same day I got responses on Twitter. At the top it said I would get a response within 24 hours so don't you think 5 days is ridiculous. I see now it says replies within minutes at the top of the page there. But I have to say this, the questions I sent on Twitter 4 days ago I copied and sent on FB late last night and I was surprised I got a response in 45 minutes although I didn't see them until this morning before I replied I had a responses within a few minutes.
One thing to note these messages were about an issue trying to order a phone and a number of questions I had with the new plans being implemented. It was nothing urgent or I would have waited inline on chat for an hour on chat. I expected maybe 1 day possibly 2 at most for these DM responses but not 4 to 5 days.
Why don't you just shut down one social media group and put the support effort into the other one. Right now the best response time is FB and suggest you go that route over Twitter. Not sure which platform would be better but something needs to be done. Currently it looks like there hasn't been activated on the FB home page coming up on a year so maybe put your efforts into Twitter helping customers.