What is your website about and why would you think, that those targeting the exact same keywords like you would want to link to you? I am currently working on a new project, that should help with link development, maybe have a look: http://review.onyxbits.de
The top 20 may be pushing it. Generally speaking anyone that ranks higher then you for your keywords should be a good link. When you get to the top of the list, you are talking about sites that carry authority and have no desire to respond to linking opportunities unless they stand to make a few bucks. Refine your approach and possibly rewrite the E-mail you are sending out. Make sure the E-mail is as personal as possible so that it does not get confused for spam. In between the frustration of trying to get those high quality links, submit to some free directories, write and submit some articles, submit to some social bookmarking sites, ask a niche related blog owner if they would do a review for your site, comment on some blogs, post some classified ads, etc. There are quite a few free links to be had out there. Granted they don't pack the same SEO punch as high quality links, but they do help. BTW, check out the backlink profiles of your competitors. In many cases you can find some free high quality links by doing some research into how they obtained their ranks. Happy link building!
High ranking sites get frequent emails (usually clearly automated) requesting backlinks so unless your email stands out in some way it will likely be ignored. Though one response from twenty on high ranking sites is actually not too bad a response rate for a standard link request. Ask yourself one question from their point of view and answer it in the emails you send out: why should they create a link to you? If you can answer that clearly - and it is not easy to do so for most sites - then you may get a higher response.
I get these every day and ignore them. Often, they are in my niche. One of these site likes to place a link to my site on some worthless link page before sending me an e-mail. I always ignore these requests. Why? It's spam. They aren't offering good links, and I know that they have lousy practices that I don't want to be associated with. What other spammy methods will this inexperienced webmaster be using? With these reciprocal requests, there's nothing in it for me, so I treat them as I do beggars-ignore them unless they are creative enough to warrant my attention. I save my giving for those who have something to offer in return. On the other hand, I respond well to such requests on this forum...because here I am seeking such connections. My advice: build one-way links until your site is strong enough to have trade value, then seek swaps with sites at that level. Those top sites don't want you crawling up their butt, anyway.
I get these also for my websites. The way I feel about it is I have worked hard for the higher ranking and unless this person is getting a lot of traffic and it is going to help me get more money then why would I link to them and make them for relevant in my niche. Most of the time our staff responds to these type of emails with our advertising media kit for the person to check out unless there traffic is close or rivals ours. Best thing to do is focus on building massive links and traffic first and try to move up in the niche before just thinking people are going to place your low PR link on their page.