Right now it sounds like you are taking them straight from tumblr to the offer? Try sending them to a 3rd party site that gets there brain outside of there normal tumblr rhythm of scroll, scroll, scroll, click, close, scroll basically.
Going straight to an offer is an interruption more so than something desired. However, if you send them to a really cool and well organized site that has exactly what they are looking for then they are more proned to stick around on the newly discovered source for what they crave. You can set up less invasive offers like modal boxes, banner ads, etc on your site and get better conversions, repeat visitors, and a long term profitable site launched from your traffic rather than burning leads so fast.