I'm sorry you're having issues! There's a couple of things that could be causing it:
Did you make sure that your ROM is completely untouched?
Make sure you haven't used any other patches on that ROM
Make sure you didn't open that ROM in a ROM editor such as SkyTemple
A good indication that this is the issue is if it says "Target Window Checksum Mismatch"
Did you forget to put ".nds" at the end of the output file name?
The Output file is "any" so you need to specifically put "EoS Remixed.nds" for it to work.
A good indication that this is the issue is if it says "Patch successful" but you can't find the file.
If neither of these are the issue, feel free to send screenshots to help me get a better understanding for what might be happening here.
Also, here's a side note: When updating to a new version of my hack, you will always need handy a fresh ROM of EoS. In order to transfer your save to the new version, make sure the save file and the game file names are the same. I personally always name my game and save "EoS Remixed", which prevents any potential save loss you may otherwise encounter.