routing tables usually aren't "cached" in the same sense that DNS caches entries.
however. Inside ISP;s routes are usually distributed by an IBGP with a couple of route reflectors, and route reflectors will drop routes if no router within the IBGP domain is advertising the route.
Routes between ISP's are usually fairly static thanks to mechanisms like graceful restart, which makes sure routes do not get dropped, even if BGP has a restart between routers. THere are various other mechanism in which to achieve this. (look up route flap dampening if you want to learn more).
however. Inside ISP;s routes are usually distributed by an IBGP with a couple of route reflectors, and route reflectors will drop routes if no router within the IBGP domain is advertising the route.
Routes between ISP's are usually fairly static thanks to mechanisms like graceful restart, which makes sure routes do not get dropped, even if BGP has a restart between routers. THere are various other mechanism in which to achieve this. (look up route flap dampening if you want to learn more).