The two big reasons startups fail are:
a) They don't provide benefit to the customer
b) Their product isn't directed towards the right customer
In context of your product, here's how I think each of those may apply.
a) They don't provide benefit to the customer
Here you have an interface to help create whole outfits. This is ostensibly valuable because most agree that a complete outfit is generally a better fashion choice that unrelated pieces of clothing. However, does this provide benefit to the customer? Well, I am not sure. For example, myself, personally, I pick out six outfits at a physical store and buy maybe one or two of them. Some of the clothes just don't fit well, others must don't quite go together (this shirt is too long for these pants). It is sort of hard to say if you have a market that would love this; if you do, I am not it. I feel there are two types of shoppers, those who want to pick out the whole outfit, and those who would rather have their entire outfit chosen for them by people with trusted fashion taste. I am actually the first one, but I still don't want this. My suspicion is that you may have built a feature and not a benefit.
Conclusion: if you haven't done market research DO IT. Run a Google Consumer Survey if you want to get something done quickly. Troll fashion forums. Question customers on their process of picking an outfit. How do they do it? What is important to them? You might find most people do not want to buy total outfits online for the reasons I mentioned above (or others). Or you may find I am an outlier.
b) Their product isn't directed towards the right customer
So, it could be that your product has value but it isn't directed at the right customer. To riff off of above (and to use examples others in this thread have noted), what if you turned the idea on its head and only had precompiled outfits (cater to men/busy professionals). Alternatively, someone mentioned price...do people really buy $700 shoes online? (Cater to market that is possibly more likely to buy outfits online).
Conclusion: Again market research can solve this for you (Q: How much do you normally spend on a pair of shoes when you buy them online? $0-50, $50-100, $100-200, $200-400, $400+).
The validation stage of your startup should happen before you've built anything. If you've done this, great! If not, get on that before you type one more line of code.
Now, smaller reasons it might not work:
a) The name
Yes, you can overcome screwy names with a great product, but it is best to try not to. I know you may have actually paid a lot for the domain, but if you did consider it lost money and move on. The real problem with it is that everyone who actually wants to use your service will go to outfits.com instead, get frustrated it isn't what they wanted (it just times out, looks like someone has been sitting on the domain for 15 years), then give up on your service. The only way cute names work is if they are both easy to say and cannot possibly be confused with another domain (i.e, not a real word, like Quora) or spelled quite different but easily distinguishable from the word they are replacing (Boxee).
b) The demo doesn't work
For me, it doesn't behave like the video--I don't see prices as I shuffle outfits. This may be intentional at an early stage but that video sets my expectations it works already. Aslo, right and left clicking don't work for me either as the instruction below the outfits suggest and get in an inconsistent state where I can't reselect. Sure, this would never make it front of customers as-is, but unless you are bootstrapping this you'll want somthing far better than this to show to investors.
c) Revealing lack of traction
Only 15 people like this on facebook? Reddit famously padded their service with fake comments and articles when they started. I am not suggesting you do that, but fashion is a trendy business and unless 1k people like this no one else is going to hit that button. My friend is a SHITTY photographer and she still has 80 pity likes from her friends for her photography business page on FB, you can get at least a couple hundred (or not show the number). Play the fashion trend game: know your audience and appear in fashion yourself.
Now some things you've done right!:
a) design
It looks good. The logo is great, the animation makes sense. It is clean, functional. Great job!
b) Gathering feedback from others
This is good you're asking us. Asking customers questions is better, but this is good. So many startups just go, hey, let's launch this thing with no questions asked and a bunch of assumptions.