Is my REALTOR doing his/her job if he/she doesn't show my house? Maybe yes, maybe no! What is the role of the listing agent?
The primary role of your listing agent is to market your home. Is your home being shown by other REALTORS? Is your home being marketed in all the areas promised to you during the listing appointment? If your answer is yes, until your home is under contract, your REALTOR is at work whether showing your house or not.
The whole purpose of entering your home in the MLS and marketing it widely is to attract as wide a pool of buyers as possible. Your REALTOR may not have a buyer for your price range, location, or size of house. However, if marketing is being done correctly, other agents will. If your state allows dual agency (an agent representing both buyer and seller in the same transaction), your REALTOR will show your house to buyers who call the agent directly from the sign or the various advertising media.
The role of your agent during the listing period is also to keep you apprised of changes in the market and to give you feedback following showings. If there are negative comments from potential buyers, you need to know so you can correct those things that can be corrected prior to the next showing. If your home is not selling, you need to know why. Is it price, condition, or location? Some things can be changed, but others can't. Often a price adjustment will compensate for some of this.
During a buyer's market, the home must be as perfect as you can make it. It may also take longer to sell your home, so if you are cooperating with your agent, following advice, adjusting price and conditions as needed, don't change agents at the end of the listing period. Renew it, and wait. If your agent is not marketing, and your house is not being shown at all, then you might try another agent and/or company.
The role of your agent once you receive an offer for your house is to present and negotiate the offer in your best interests. Your agent is your seller representative all the way to closing, ensuring your understand and adhere to the terms of the contract. If certain inspections are required by the seller, your agent will assist with this.
I've heard sellers say that their agent must not be working on their behalf because he/she never shows the house. I hope you will take a look at the other activities that are being done to market the house and get it maximum exposure before making that assumption.