H4 is H1 dependent

There's very little you could do in this situation. As you know, H4 status is entirely H1-dependent and expires when H1 runs out. You may want to find out why your hubsand is not willing to renew his visa. If, for example, he is not interested in staying in the US while you plan to stay here. Then what at issue becomes very personal: it's your marriage, not your immigration status, that is at issue.