The free version of My Boy! emulator won't let me continue from my last save?

_{Comments originally posted under the question converted into a wiki answer. Credit: Mr. Mendelli:}

I did some extensive testing, and have made some discoveries.

First, ensure that the ROM name and save names match (excluding their file extensions). So for example:

Gamename.gba
Gamename.sav 

If the game is stored on the device's internal storage, the save file must be in the same directory as the ROM. If the game is stored externally, i.e. an SD card or USB drive, the save file will be written to the following location:

storage/emulated/0/MyBoy/save/ 

This means that if your game is in storage/emulated/0/Download/, then the save file will be somewhere in that folder. If it is not, than you have either lost it, it's name does not match, or it has been deleted.

I place my games on my microSD card in: /Games/GameBoy Advance/. I have noticed that in most (not all) similar cases, the user has misplaced or accidentally deleted their save due to disorganization or storage clutter. I always advise keeping any devices storage as neat as possible to avoid misplaced data and files.