Yes. Search engines sometimes de-index some pages after indexing. However they don't de-index quality backlinks.
Keep building links - Quality backlinks

You can't relay that much anymore on yahoo site explorers information. Try MajesticSEO better.

Also beware that Yahoo Site Explorer won't ever show all indexed links, there is also a percentage of information it likes to keep hidden, therefore any SEO analysis tools scraping Yahoo results won't show ALL inner pages or backlinks even though they are indexed and valid.

I believe it is a security thing, so you can't FULLY reverse engineer someones site. It took me a while to figure that out!

Try to improve back links and do Social bookmarking of your website. Every thing will be set. Don't worry.

Yahoo explorer is up and down on a daily basis. Yahoo also counts dofollow and nofollow. It is a nice checker, but it so up and down from one day to the next it is difficult to get a big picture from it. Still for free it is nice to check, and is much better than bing, and even could be considered better than google since google tends to hide many backlinks from you even in webmaster tools.

maintaining the off page SEO of your website is part of the process that website owner must know.

Most website owners think that once their site is in 1st page it does not need to be maintained. Very wrong