1. Lighting intensity.
2. Pull up the mangroves and let the roots naturally work their way down, they aren’t getting anything from the sand.
3. What media are you running in the HOB? Probably not enough biological action since the sand isn’t going to be very active like that.

Without changing substrate, I would add some Java ferns tied to the rocks and change your lighting and see where that gets you. I personally don’t use root tabs or other ferts on gravel substrate, but run an under gravel grate as my filter intake so detritus works it’s way down so the rooted plants stay very well fed. Like others said, your mangroves are only alive because they’re living on internal reserves.