You are surely going to have to take a look in the service charge agreement to see what it covers (and I don't mean 'gates' - it won't be that specific).
Service charges typically cover the direct maintenance charges, incurred year-in year-out, as well as a 'sinking fund' (or some other such wording) that is intended to cover the costs of occasional capital replacement/refurbishment.
The HA presumably wants to try and tag it on that. I think they may succeed in being able to do that.
Let's give you another scenario: if an uninsured driver hit the gates, would the HA expect to fork out to replace the damage, or would it expect to fund it from the general service charge pot? The general pot surely? I think it is a similar situation, except that you feel that the HA has caused the issue by recklessness (or whatever). I think you'd have to challenge that in court to win.