Does anyone know how often Google re-spiders URLs that currently exist in their index? I am specifically referring to an index where the keywords used to find the link no longer exist in the page. How long can one expect to wait before the link goes away. I have been able to remove the cache and the description text from the google listing using the URL removal tool but the link text still remains even though it is no longer relevant to the search criteria.
that depends on links, if you re-link pages, google index more fast, where as that depends on site activeness that how can google treat old pages.
Ensure that the pages return a status of either 404 (not found) or 410 (gone) in the header. These status codes tell Googlebot that the requested URL isn't valid Its been said that after fresh crawling Google removes the links from deleted pages from its index... But it takes huge time, so, you have to remove such pages from Google index manually.
If those link return 404/401 status, then you can use URL removal request from webmaster tool. thats the only fast url removal option.
2 days? I have pages that 404 from 5 or 6 YEARS ago still popping up in google searches. Its incredibly annoying.
Its because your removed pages had backlinks from different sources, which is why they are appearing in the search results. You need to remove them manually from the index using Google removal tool.