I've been having the same problem. It's hard to get a file if only one person has it or if it's really popular. Grandpa1 gave me this explanation and it really helped:

"I guess i am going to have to go into a little more detail in my explanation. OK we will use me as an example now I share around 400 files most of the time when I am at home I leave LimeWire on 24/7 when I am there. But I work in construction therefore I am on the road allot thus LimeWire is off when I am not there.
When I am sharing I allow 10 slots for people to download from me. I have cable and can upload at 45kb so 45/10 = 4.5kb per person. There are always 10 downloading from me and 10 waiting to download from me so that means no one else is going to be able to download from me until someone finishes. Now if there are lets say 1000 people looking for any of the 400 files I am sharing that means your odds of connecting to me are 1 in 1000. With those odds the likelihood that you will ever connect to me is somewhere between slim and none.And if you do you will only get 4.5kb download speed..
(The moral to this story) If you choose files that only have 1 source you are asking for it to take a long time to complete in most cases, if ever, and slow download speeds. Hopefully this will fully answer your question. There are stickies on how to improve your upload and download success with LimeWire if you want to improve your performance with LimeWire read them."

So basically, there's no way to speed up your download (I speak from experience). Just keep searching and eventually it will connect, if only for a short while. My advise is, keep your computer on 24/7, keep searching, and be very patient.