All of the links that I have built up over the past 2 months slowly disappeared from Google Webmaster tools until I am left with none. Why is that? Does Google only count links for a limited time?
Are the links physically there? Check your site information on google, use "info:yoursitedomain.com".
If I do info:thesite.com then only a few show up. Previously there were dozens and dozens there. They still show up on Yahoo and haven't disappeared. It just seems like Google decided to not count them or is no longer noticing them.
I suggest you keep building backlinks. Google only count quality backlinks and will only show such backlinks in webmaster tools. For example, if you get a backlink from a PR5 or PR4 page, then you will always see it in webmaster tools.
I also have some sites for which the links have disappeared in Webmaster Tools. The links that have disappeared are still present for other sites that I have in Google Webmasters though, i.e. from external Page X for example, I have links to 2 of my sites - the link to one site has disappeared while to another it is still present. Weird!
I find external links are like the swell, they come in and then go out again, neverless they will always be in motion if you continue to build them
At the end of the day, quality external links are what will get you ranked in google. There is no substitute.