Back links are semi-permanent. In some cases links may get removed by the site owner or become “broken” or “lost” due to various reasons. The most important thing to note about back links is that once you start and especially when you stop building them - you drop (in rankings) – This is called “the Google Dance” - Google wants to make sure that you're link juice is consistent and “natural-looking” – if they see a big spike in back links and then nothing else for a week or two or months – they’ll “drop” your site to “test” it and if there has been proper back link building and structuring going on.
If you've been utilizing back link building services and suddenly stop, your site’s rankings will definitely drop and stay there if no more links are being continuously built to it. You may recover some with good content that’s well optimized with your keywords if you have the proper on-page optimization but overall chances are you won’t reach page 1 until you begin actively building links again.