You may because there is little time left on his visa and your visa is dependant on his. The two of you should consult with an immigration attorney who can make adjustments for both of you in a sequential manner that works for both of you.
It should not be denied for the reason you state but you can only obtain H-4 status for the remainder of your husband's H-1B current term.
San Francisco Immigration Attorney for removal defense, all work visas and avenues to permanent residence, investors, and naturalization. Call 415.834.0600 for free phone consultation - mention Avvo! 235 Montgomery Street, Suite 728, San Francisco, CA 94104 / www.lawbridges.com
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.