Configuring two NS entries is pretty standard, so surely most resolvers try one of the two, and if it's down try the other one? What else would be the point of having multiple nameservers? Then you just have to get two nameserver providers and make sure their settings stay synced, and point your domain to one nameserver from each.
Of course that requires the server to properly fail, i.e. stop responding to requests. That doesn't seem to be the case here