Dear friend,
I really understand and sympathize with how you feel. You have had your little pal for about three years and taking to vets to be put down would be so very hard. Once a pet stops eating it is because he has given up and does not want to live anymore. He is either sick or tired and he is going to refuse food or water. He is not "coming apart" - his little systems are just shutting down so nothing is quite right.
I would suggest you take him out of the cage and hold him. Spend as much time with him as possible. Say goodbye to your little friend in your own time and in your own way. I know you will miss him very much.
If you have any more questions or want to talk more about this - I will be here for you, just let me know.
Sincerest best wishes,
Terri