My take on it is. They know what needs to be done, they are doing it, however they can not pin the completion of the test and clearance down to a set date.
"Cannot" or "will not"? The way I see it, does Alton Towers want to publicly give a set date where they will have completion of the ride's prep done and all relevant paperwork to sign off the site? As I see it, there are two potential things that can happen if AT announce a fixed date for reopening:
1. Delays either by internal or external personnel mean that AT miss opening, which could cause some backlash through the media (no doubt they'll sensationalise that somehow or another).
2. AT meet the deadline/fixed date and the ride re-opens, to be greeted by a number of press outlets who travelled there to get the exclusive story who had been told the fixed date.
If AT are going to announce it at all, they will announce it through either a press conference, video (including NV riding the ride first as promised), or through a press statement the morning BEFORE it re-opens. In my opinion, they won't announce it at all, and they'll just let it silently re-open the ride and let it run for the day. Only after the ride has been in operation all day would they release a statement/hold a press conference to answer any potential questions from the press. Whatever angle you look at it, AT are going to get bad press from this, but they need to work towards minimising the bad press as much as possible - they can do this by making it absolutely crystal clear that additional safety steps have been incorporated into the ride's already vigorous safety checks, to further prevent an incident like this happening again. They should also mention what that their internal investigation has concluded (eg. human error combined with an unique set of circumstance - eg high winds I'm presuming for the stall, and system override to reset the ride and get it moving again) and ensure that it is made clear that thorough training has been taken place over the last few weeks (hence the testing) to ensure that staff are fully competent in operating and working on the ride. Mention that they're continuing to support the victims and that they discussed the reopening with them before they made the decision to re-open the ride.
Ps. changing the wording that the Social Media team have put out recently is a positive step forward considering recent events, although "foreseeable future" was suitable enough for what it was needed for, as sick and tired we all was of seeing it! I do feel bad for their Social Media team however, cannot imagine how difficult it's been for them responding to people about it for the last 3-4 months. Let's hope that a reopening is near!