I did an internship for 1 month (that was all the time I had in the particular uni holidays I had arranged them for) and I kept on being told by the company that I really should have tried to be there longer at least for 2 months so I could really see what was happening, particularly so I could see projects going from beginning to end rather than just the finished product or the beginning, if that makes sense.
I've sent so many emails out for internships and only got a small amount of replies back, and some were kind enough to say they didn't have internships for the period I was interested in or so forth, but the HUGE majority didn't even reply at all. As fashionistasista said many of these companies receive bucket loads of emails per day not just for internships but other people cold-calling for entry level/assistant jobs so they don't have enough time to personally email everyone to explain why they couldn't get hired.
For tips on getting internships, I'm with gia0202 and go for something that's smaller but still highly respected - WWD/Lucky/Glamour/etc is definitely not going to look shoddy on the resume, eg in regards to WWD it in fact shows that you know a bit more about fashion than just Vogue and Teen Vogue. Also know the companies inside out - each magazine has its own voice and perspective and I think it's important to understand where they are heading and what they are trying to do and what sort of image they're putting across.
Also getting experience anywhere is really good, whether working in fashion retail or work experience in something, as long as it shows that you're willing to put yourself out there. I've interned at a really small PR firm (small like, it has less than 6 full time people working in the office!) but I got a lot of really good hands on experience with everything from events, organising the clothing, being the door b*tch at cocktail launches, guest lists, etc - though it did help they had some absolute killer clients like Cartier so that does help on the resume.
Best of luck!
