I am applying to a few different masters' programs this fall after having applied to a different program last year. In the end, I decided not to pursue that option due to financial reasons. I graduated from my university in May 2014, and I have visited many of my professors during their office hours while I was a student there. Of course, I only made recommendation letter requests to professors in courses that I did well in. Last year, when I was applying to another program, it was relatively easy to obtain recommendation letters from the professors I made requests to. However, this year is different. I explained my change of direction to the professors who wrote my recommendation letters last year. Except for one professor, the other professors don't even bother responding to my emails. In cases when I am requesting recommendation letters after graduation, do I have visit professors directly and have a conversation with them? If that is the case, I am unable to do that because I am currently outside of the US. Also, am I expected to give them a gift at the time I am making such request? I want to know what I may be doing incorrectly.
I don't think you're doing anything incorrectly. Sometimes people get busy, sometimes people are thoughtless and inconsiderate. I'm afraid you're going to have to use a combination of persistence and politeness. The tricky thing with the politeness is that you don't want to lay it on too thick -- as that in itself can get annoying.
Please consider using a combination of email and phone.
If things are still going badly after about two weeks, then I think it's time to contact a department secretary, dean, assistant chair or assistant chair.
I can see that in some departments it might be easier to pester someone by knocking on their door, but that really shouldn't be necessary; and you can use the department administration to accomplish the same thing.
(As mentioned in a comment -- please, no gifts. It's not the custom in the U.S. and therefore would be too weird.)
Definitely do not send gifts! That is wildly inappropriate.
tl; dr - Send them a gentle reminder.
When I was in undergrad, I intended to go to medical school. I took the MCAT, applied (with letters of recommendation), got interviews and then I had a change of heart. I had a realization that I never wanted to tell a parent that their child had died (e.g. in a car accident / overdose / aneurysm / etc). It was just too heavy for my 22 year old self. Instead, I entered the workforce as a software engineer. I liked parts of the job and learned a lot, but I wanted to ask my own questions and pursue my own interests. After some thought I decided to apply for PhD programs in neuroscience.
When I recontacted one of my important letter writers to ask for a new and different letter, he questioned my commitment to the PhD, remarking that I had had a change of heart before. I was pretty surprised and a bit hurt, but I responded thoughtfully to him, explaining the process that I went through, and that I was sure this time. He ended up apologizing to me (!) for forgetting what it was like to be a 22 year old. He not only wrote me a great letter, but personally called my future PhD advisor to put in a good word for me. We remain friends to this day.
In summary, young people are still finding themselves. Many successful academics change direction in their careers. Many great computational neuroscientists were physics or math PhDs that reinvented themselves.
So, send them a gentle reminder. Include a short explanation of your change of mind and why you are sure you are committed to this new path.