Does my employer have to honor my contract?

The issue is: who was the contract with, and how was the business sold.
Business can be sole proprietorships or partnerships, on the one hand, where the owner(s) are the business; or they can be LLCs or corporations, where there is a separate business entity which is it's own legal "person." A contract is only with the "person" who signed it. So if your employer had been a sole proprietorship or partnership and the owner(s) sold the business to someone else, your contract was with the old owners personally, not the new owners--and so the new owners are not bound by it.
If your employer had been an LLC or corporation, then IF the LLC or corporation itself--that is, the "person" with whom you were contracted--was acquired by someone new, then the contract is still in place and effect: the contract was with the LLC or corporation, you are still working for the LLC or corporation (it just has new owners), and so the contract is valid. In this case, you could sue for "breach of contract" to enforce the terms of the contract, or get compensation for its breach/violation.
But if the LLC or corporation for whom you'd worked was NOT itself acquired by the new owners, who instead just bought the "assets" of your old employer (e.g. contract, name, intellectual property, "good will," accounts receivable, equipment & inventory, etc.), the new owners are not bound to the contract--they never signed it. Rather, your contract remains with the old LLC or corporation which, unfortunately, you are no longer working for and probably does not have any assets or operations (and may not even exist any longer).