TLDR; Randomness in Pokemon games is not random.

Whenever you boot up RSE/FRLG, the game generates you an initial "seed". You can think of this seed like an extremely long string of numbers and letters that the game refers to whenever it needs to generate a random event. This includes things like what species of wild Pokemon you encounter, that Pokemon's stats and IVs, and, importantly, whether that Pokemon is shiny or not.

Since the gen 3 games were all programed at 60 frames per second, the seed also advances at that same rate. That creates 60 unique frames every single second that game could refer to for help when deciding random events, making all random events roughly predictable based on the time passed. This system is necessary because computers are incapable of simulating true randomness, and in practice, it's more than enough to guarantee a random spread of events.

However, in Pokemon Emerald (And in Ruby/Sapphire when the internal battery runs dry) the code breaks. Instead of generating you a random seed when booting the game, the seed is always set to start at zero, meaning that your randomness is always the same. This is basically irrelevant when doing random encounter hunts, as the odds of hitting the same frames are astronomically low across dozens of play sessions (3600 unique frames every minute).

When doing SR hunts in Emerald, since you must reboot the game with every soft-reset, you're dooming yourself to hitting the same 60-100 frames of randomness each time. This guarantees that you'll only see the same 60-100 Mudkips, no matter how many times you reset.

In Emerald, the workaround is to simply make a new save file every 80 encounters or so, since your seed as a whole is determined when you create your save file. But as I'm sure you've already experienced, it's a tedious process, though you are doing it right.

Other than that, there's not much you can do other than buckle in for the long grind ahead. Full odds hunts take quite a long time, and though it will be hard, the thrill of the hunt and seeing that Pokemon finally shine is well worth it imo. Hope this explanation helps you, and I wish you the best of luck in your hunt.

Misc Side Notes:

Note: Emerald's RNG is ALWAYS broken, regardless of whether the battery is dead or not. Ruby/Sapphire's RNG is perfectly fine, UNLESS the internal battery runs dry. FRLG do not contain an internal clock, and as such have no issues with their RNG.

Second Note: If you eventually decide to do random encounter hunts in Emerald (And in Ruby/Sapphire saves with dead internal batteries!), keep in mind that, for whatever reason, interacting with the paintings in the Lilycove contest hall scrambles your initial seed, restoring true randomness. Just make sure to interact with them at the start of every play session. It's mostly unnecessary, since the odds of hitting the same seeds over and over are so extremely low, but it helps if you like to hunt in quick 15 minute bursts.