Yes, the further away you get from the router, the slower the speed, and you can loose connection if you go too far. Walls, etc.. cause huge drops in signal strength. And also how the antenna is pointed will usually give you a greater side to side than up and down signal.
You may be able to fix this by getting a higher-end wireless router or a wireless access point to extend the range. There are tons of posts on here and other sites about extending wireless range.