Is it inappropriate to ask a professor for multiple letters of recommendation (at different times)? I'm applying for an Honors program within my college during my undergraduate degree, and need a letter of recommendation from a professor in my specific field. However, because there are few professors in this field who have taught my classes, I'd need to ask someone who already provided me with a letter last year (for an award, which I won, if that makes a difference). 

I know the question of "how many recommendation letters" was answered here, but I'm referring to letters requested at different times, far apart. Will this individual, if they remember me, likely be annoyed that I returned to them? Do professors save these things (perhaps they could recycle the same letter)?
It is not a problem in principle to ask for letters of recommendation at different periods of time. However, one should certainly make an effort to keep the recommender aware of career developments since the letter was originally written. (However, the relevant time scale over which old letters of recommendation become "outdated" is much longer than one year!)

For the most part, in the digital age, we keep letters of recommendation "on file" and recycle and refresh the content as warranted, so it's not a herculean effort to write a "new" letter after a while.