Can a franchisee terminate a franchise agreement if the franchisor has failed to perform its contractually obligated tasks?

There is no way to answer your questions with any sort of confidence without making a number of assumptions.  The short answer is "It depends on what the contract says."  What constitutes a failure to perform, or a material breach, or whether there has to be an opportunity to cure, or whether there are preconditions to certain remedies (up to and including termination) are all very dependent on the precise language of the contract.  Even where there are industry standards and customs of practice and dealing, these can be modified by the actual agreement you signed in many cases.  The bottom line is that you need to bring the agreement to an attorney in your jurisdiction.

The best answer is maybe.  As the other poster stated, the degree of the breach is important.  Further, you need to know what YOU mean be termination.  Frequently, equiptment belongs to the Franchisor not the Franchisee.  You may also have lease, loan or amortization agreements which will effectively block your attempt to terminate the relationshiip.  It is not like you can reopen the following day doing the same type of business.  You might have to walk away entirely.  There are several other concerns.  +1 on the advice to have an attorney look at your specific documents.  In circumstances like yours, I almost uniformly advise my clients to get a court order establishing the rights of the parties.  Their are various ways to do this depending upon your jurisdiction.  The botom line is that this is a VERY big move and you might take yourself from the frying pan into the fire if you are not careful.

As a general matter, if a franchisor has violated its obligations under the franchise agreement, the franchisee will have the right to seek a court order requiring performance, seek monetary compensation, or terminate the agreement. However, that last recourse--termination--will generally only be available when the other party's breach is a "material"--or significant--one, going to the heart of the agreement. Lesser breaches would most likely give rise only to a claim for damages (money) or provide grounds to seek declaratory or injunctive relief requiring specific performance of the agreement. To understand the rights available to the franchisee in this specific case, it is necessary to discuss the matter in depth with a business attorney, one who can review the franchise agreement.