I don't think the period over which raspberries remain healthy and productive is fixed. Rather it is an issue of trying to keep them healthy with proper feeding and care. If you can avoid serious pests and diseases, especially virus problems, I've heard of them going for 15 years.
Alas it sounds as if your's are deteriorating. In which case new canes in a different spot would be ideal.
If they must go into the same ground most books recommend replacing all the soil to at least one spit deep. I do not have any direct experience of doing this so cannot confirm how well it would work.
It might be worth giving them one more year - provide a lot of TLC by pruning to open up next year's growth and make it very airy, give them a good feed and see how next year goes. No improvement? Perhaps then go nuclear and replace the lot!