Okay, the first answer doesn't help too much with answering the question, so I will give my answer, as I have personal experience with Emerald's RNG issues.
Yes, the RNG in Emerald is broken, which makes soft resetting targets completely pointless unless you have an "early shiny frame", meaning that the numbers being rerolled in your game, depending on your ID and SID combo, one of them has been programmed to produce a shiny. However, given that you've been resetting for months, the chances of you having an early shiny frame are pretty much impossible. You have been hitting the same frames over and over again, reproducing exact copies of the same Rayquaza without even realizing it.
There is a way to get yourself a shiny Rayquaza without going into the games programming and manipulating the RNG, however, and that is using the run away method! Here's what you do: you MUST keep your game on at all times (having a charger is important). If you keep your game on, your Emerald game will constantly be making new frames for you to hit, as resetting the game also resets the frames in the exact same order they were hit before, hence why soft resetting is considered impossible without an early shiny frame. Anyway, you can encounter the Rayquaza, and run away from it. It may seem like it's gone, but it's not! You just exit the room that Rayquaza was in, reenter, and the Rayquaza will be back! You encounter it again, and repeat this process until you get your shiny! Since your game isn't being shut off, your chances of finding a shiny frame and your shiny Rayquaza are the exact same chances of any other game, 1/8192.
Edit: I have confirmed with a friend that keeping the game on at all times isn't exactly necessary. This is because after a certain length of time, you are certain to have passed a "shiny frame" at least once, and it is very likely that you could miss it. You should at least have your game on and running away from Rayquaza for a couple hours at a time, and it's safe to turn it off and try again another time.
Source: knowledge and experience (I messed with the RNG to get a shiny on Emerald myself before) and my friend who has hunted on Emerald and gotten shinnies by doing what I wrote in the edit.
I hope I helped!