@alejandro_contreras,
Your first step should be to check the ULS logs while you try to start the sync service and see what errors you see. Did this used to stay started? It sounds like a permissions problem, but there could be many others. Check out Spence Harbar's writeup to ensure you have everything correct:
http://www.harbar.net/articles/sp2010ups.aspx
If you gather some ULS logs and errors feel free to post, but it sounds like you a full re-check of everything and configuration is in order. If you do all that and it still errors, we will need any errors you get when starting.
