How/when should I ask my supervisors' for a reference letter? I'm currently a fourth year undergraduate student graduating this year. I'm taking the upcoming school year off to travel, so instead of applying to grad school during my fourth year like most students, I will be applying this upcoming September (when I will have graduated).

I worked with two professors this school year doing research, one of which I got a publication out of. I plan on asking both for reference letters for my graduate school applications.

Both profs seem to like me and are happy with my work. However, I won't be actually applying to grad school until late this year (probably September-December), so I'm worried if I ask for a reference later in the year, they will have forgotten a significant chunk of their experience supervising me and my contributions. 

I want to get a letter out of them now when I'm still fresh in their minds and can get a great recommendation out of them. I'm sure they'll give me a positive one either way, but I feel like if I get one now it'll be a lot stronger, where as if I do it several months in the future, considering how busy they are, I probably won't be nearly as well remembered and my letter will be a lot more generic.

I wasn't sure if this is appropriate to do, and how I should go about doing this, so I was hoping I could get some advice on this. Both profs work in ECE (electrical and computer engineering) and the programs I will be applying to will be a combination of ECE programs and computer science programs.
Inform them about your plans now and let them decide what works best for them.

You may be right that they will have forgotten you by the time you apply (depending on how much you worked together). But on the other side, the best LORs are specific to a position you are applying for and should be tailor written, "generic" LORs may not be as good, and some people may not want to write one without knowing what they are going to be for.