Don, it does sound like your drail tile may be silting in. You could try running a hose with a drain cleaning bladder attached down the line, but this is usually a fruitless effort. You can only get a hose to go so far before it won't go any further, and when the tile begins silting in, it will often be doing so for quite a distance. Do NOT use a snake; this can damage the line.
What does work very well is a cleanout process you can have done by Roto-Rooter. It uses water under hydraulic pressure to cut loose silt as it draws the line through the drain tile. I've used this method for several of my customer's homes, and all were successful. Good luck